An Optimization of Statistical Index Method Based on Gaussian Process Regression and GeoDetector, for Higher Accurate Landslide Susceptibility Modeling

Cen Cheng; Yang Yang; Fengcheng Zhong; Chao Song; Yan Zhen

doi:10.3390/app122010196

An Optimization of Statistical Index Method Based on Gaussian Process Regression and GeoDetector, for Higher Accurate Landslide Susceptibility Modeling

Cheng, Cen;Yang, Yang;Zhong, Fengcheng;Song, Chao;Zhen, Yan 2022-10-11 00:00:00 applied sciences Article An Optimization of Statistical Index Method Based on Gaussian Process Regression and GeoDetector, for Higher Accurate Landslide Susceptibility Modeling 1 , 2 , 3 1 , 2 , 3 , 3 , 4 5 1 , 2 Cen Cheng , Yang Yang *, Fengcheng Zhong , Chao Song and Yan Zhen State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China School of Geosciences and Technology, Southwest Petroleum University, Chengdu 610500, China Spatial Information Technology and Big Data Mining Research Center, Southwest Petroleum University, Chengdu 610500, China Sichuan Xinyang Anchuang Technology Co., Ltd., Chengdu 610500, China HEOA Group, West China School of Public Health and West China Fourth Hospital, Sichuan University, Chengdu 610044, China * Correspondence: yy_swpu@swpu.edu.cn; Tel.: +86-18681279063 Abstract: Landslide susceptibility assessment is an effective non-engineering landslide prevention at the regional scale. This study aims to improve the accuracy of landslide susceptibility assessment by using an optimized statistical index (SI) method. A landslide inventory containing 493 historical landslides was established, and 20 initial inﬂuencing factors were selected for modeling. First, a combination of GeoDetector and recursive feature elimination was used to eliminate the redundant factors. Then, an optimization method for weights of SI was adopted based on Gaussian process regression (GPR). Finally, the predictive abilities of the original SI model, the SI model with optimized factors (GD-SI), and the SI model with optimized factors and weights (GD-GPR-SI) were compared Citation: Cheng, C.; Yang, Y.; Zhong, and evaluated by the area under the receiver operating characteristic curve (AUC) on the testing F.; Song, C.; Zhen, Y. An Optimization of Statistical Index datasets. The GD-GPR-SI model has the highest AUC value (0.943), and the GD-SI model (0.936) also Method Based on Gaussian Process has a higher value than the SI model (0.931). The results highlight the necessity of factor screening Regression and GeoDetector, for and weight optimization. The factor screening method used in this study can effectively eliminate Higher Accurate Landslide factors that negatively affect the SI model. Furthermore, by optimizing the SI weights through GPR, Susceptibility Modeling. Appl. Sci. more reasonable weights can be obtained for model performance improvement. 2022, 12, 10196. https://doi.org/ 10.3390/app122010196 Keywords: landslide susceptibility; statistical index; Gaussian process regression; GeoDetector; Academic Editor: Fernando Rocha recursive feature elimination Received: 18 August 2022 Accepted: 3 October 2022 Published: 11 October 2022 1. Introduction Publisher’s Note: MDPI stays neutral Landslide is a natural disaster that can be deﬁned as the movement of rock, dirt, with regard to jurisdictional claims in or debris down a slope [1]. Landslides are common around the world and commonly published maps and institutional afﬁl- occur in mountainous areas, posing varying degrees of threat to people’s life and property iations. safety [2]. Froude and Petley [3] conducted a temporal and spatial analysis of the global data set of fatal non-seismic landslides from January 2004 to December 2016. Their data showed that 55,997 people were killed in 4862 different landslide events, with Asia being the major region suffering from landslide disasters. In addition, the number of landslides Copyright: © 2022 by the authors. caused by human activities is increasing. Landslide susceptibility mapping (LSM) is an Licensee MDPI, Basel, Switzerland. effective risk assessment method used for landslide prevention and control. In recent This article is an open access article years, various models have been applied to landslide susceptibility mapping. Improving or distributed under the terms and innovating these models to obtain more accurate mapping is a major difﬁculty in landslide conditions of the Creative Commons susceptibility assessment studies [4]. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ At present, quantitative models applied to landslide susceptibility assessment can 4.0/). be divided into four categories: physical-based models, opinion-driven models, bivariate Appl. Sci. 2022, 12, 10196. https://doi.org/10.3390/app122010196 https://www.mdpi.com/journal/applsci Appl. Sci. 2022, 12, 10196 2 of 28 statistical models, and machine learning-based models [5]. Physical-based models are suitable for local-area scale mapping and analysis and have a strong landslide warning abil- ity [6]. However, because of the large amount of required ﬁeld survey data, the evaluation process is complicated and expensive, making it unsuitable for landslide risk evaluation in large-scale areas [7]. Opinion-driven models such as the analytical hierarchy process [8], step-wise assessment ratio analysis [9], and analytical network process [10] have also been applied in numerous landslide susceptibility studies. In these models, evaluation is based on existing expert knowledge, and the evaluation process does not follow a consistent standard, making quantifying the results difﬁcult. Bivariate statistical models are infor- mation mining methods based on statistics, such as frequency ratio (FR) [11,12], statistical index (SI) [13], certainty factor (CF) [14], and evidence weight [15]. This type of model is straightforward to implement, easy to understand, and has satisfactory prediction perfor- mance. More recently, due to the growing development and maturity of big data mining techniques, machine learning has become a hotspot in the ﬁeld of landslide susceptibility research owing to its powerful data analysis and prediction abilities. In essence, machine learning and multivariate statistical analysis intersect. Further examples including logistic regression (LR) [16,17], random forest [18–20], support vector machine [21,22], artiﬁcial neural network [23,24], and other algorithms, have been applied in landslide susceptibility assessment with advanced prediction performance. In addition to the above models, hybrid methods utilizing multiple model types also achieved excellent performance [25,26]. Statistical models and machine learning-based models are the most widely used quan- titative analysis models. However, both types of models have speciﬁc disadvantages. Although machine learning-based algorithms have high predictive accuracy, their underly- ing rules are complicated and difﬁcult to express intuitively. Hence, they are not conducive to analyzing the relationship between landslides and factors [27,28]. Bivariate statistical models overcome this problem [29,30], but they employ a certain irrationality in the distri- bution of weights, which decreases their predictive accuracy. According to Tobler ’s ﬁrst law of geography, objects that are close to each other in geographical space are also more closely related [31]. For models such as SI and FR, each class has the same weight. For continuous factors such as altitude, this leads to sudden changes in the weights at the boundary of different classes, and similar factor values have completely different weights. In the same class, different factor values have the same weight, which is unreasonable [9,32,33]. Model quality is directly related to the accuracy of its evaluation, but the selection of inﬂuencing factors also affects landslide susceptibility evaluation results [34]. At present, popular factor screening methods include the information gain ratio [35], variance inﬂation factors [36], recursive feature elimination (RFE) [37], rough set [38], principal component analysis [39], Pearson correlation coefﬁcient [40], and Spearman correlation coefﬁcient [41]. In addition, the GeoDetector method proposed by Wang et al., (2010) effectively uses spatial information of data to identify the primary factors affecting a certain phenomenon [42,43]. This has been innovatively applied to landslide susceptibility analysis [44,45]. This study aims to develop a hybrid optimization method for the SI model. This method optimizes the SI weight through GPR, which can avoid the irrationality of the bivariate statistical model mentioned above and improve the accuracy of landslide suscep- tibility assessment. In addition, the integration of GeoDetector and RFE is used to further optimize landslide inﬂuencing factors used for modeling. The area along Duwen highway in Sichuan Province, China, was used as the study area. A landslide inventory was created, and the overall performance of the SI model, SI model with optimized factors (GD-SI), and SI model with optimized factors and weights (GD-GPR-SI) were compared and analyzed. 2. Materials 2.1. Study Area The study area stretches along the Duwen Highway (see Figure 1), located in Sichuan 0 0 0 Province, China. Its geographic coverage is 103 36 E–103 64 E longitude and 30 94 N– 0 2 31 52 N latitude, with an area of 922 km . The Minjiang River, an important branch of the Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 of 30 2. Materials 2.1. Study Area The study area stretches along the Duwen Highway (see Figure 1), located in Sichuan Province, China. Its geographic coverage is 103°36′ E–103°64′ E longitude and 30°94′ N– Appl. Sci. 2022, 12, 10196 3 of 28 31°52′ N latitude, with an area of 922 km . The Minjiang River, an important branch of the upper reaches of the Yangtze River, is the main river in the study area. Many hydropower structures have been built along this river to provide energy for nearby areas. The Duwen upper reaches of the Yangtze River, is the main river in the study area. Many hydropower Highway is built along the basin. In addition, many roads are distributed throughout the structures have been built along this river to provide energy for nearby areas. The Duwen study area. On 12 May 2008, an earthquake with a magnitude of Ms 8.0 occurred in the Highway is built along the basin. In addition, many roads are distributed throughout the study area, leading to a large number of secondary disasters, including a large number of study area. On 12 May 2008, an earthquake with a magnitude of Ms 8.0 occurred in the landslides [46]. study area, leading to a large number of secondary disasters, including a large number of landslides [46]. Figure Figure 1.1.Landslide Landslide inventory inventory map map and and location locatioof n of the the study stud ar y ea: area: (a)(location a) locatio of n Sichuan of SichuPr an ovince Province in China; in Chi( n b a); location (b) location of of the study the stuar dy ea; are (ca ) ; study (c) study area area and a landslide nd landsli inventory de inventmap. ory map. The altitude in the study area varies signiﬁcantly. The lowest altitude is ~734 m, and The altitude in the study area varies significantly. The lowest altitude is ~734 m, and the highest altitude is ~5280 m, providing favorable conditions for landslide formation [47]. the highest altitude is ~5280 m, providing favorable conditions for landslide formation The study area has a continental monsoon climate. The annual rainfall is 800–1300 mm [45]. [47]. The study area has a continental monsoon climate. The annual rainfall is 800–1300 There is a wide range of stratigraphic outcrops in the study area, primarily Triassic in mm [45]. There is a wide range of stratigraphic outcrops in the study area, primarily Tri- age. The area has good vegetation coverage and is primarily covered with forests. Hard assic in age. The area has good vegetation coverage and is primarily covered with forests. rocks are mainly distributed in the north and middle of the study area, while soft rocks are Hard rocks are mainly distributed in the north and middle of the study area, while soft primarily distributed in the southern regions. In addition, the exposed bedrock is primarily rocks are primarily distributed in the southern regions. In addition, the exposed bedrock composed of granite, diorite, limestone, phyllite, sandstone, and granite [48]. is primarily composed of granite, diorite, limestone, phyllite, sandstone, and granite [48]. 2.2. Landslide Inventory An accurate landslide inventory map is the basis for effective landslide susceptibility assessment [35]. Landslide data in this study originates from a 0.5 m resolution multi- band remote sensing image obtained by the Pleiades satellite in 2014. Based on remote sensing image interpretation and ﬁeld investigation veriﬁcation, 493 historical landslides were identiﬁed in the study area. According to the Varnes classiﬁcation system [49], the Appl. Sci. 2022, 12, 10196 4 of 28 landslides in the study area mainly belong to rock fall, and a small part of them belong to debris fall and debris ﬂow. The total landslide area is 15.6 km , accounting for 1.69% of the study area. The average area, maximum area, and minimum area of landslide are 2 2 2 0.032 km , 0.991 km , and 0.00041 km respectively. Roads in the study area are the main infrastructure that suffers from landslide damage, causing enormous economic losses. In this study, the geometric center of the landslide surface is taken as the landslide point. According to the data and prior knowledge, a 30 m 30 m grid was selected as the basic evaluation unit. Consequently, 1,024,455 grids were created for the study area, and 493 landslide points were located in different evaluation units, with a total of 493 landslide units. By random sampling, 70% (345 landslides) of landslides were used as training data for modeling, while the other 30% (148 landslides) were used for testing. A landslide inventory map was established using these data (see Figure 1a). 2.3. Landslide Inﬂuencing Factors The selection of inﬂuencing factors is a key step in landslide susceptibility model- ing [30]. The formation mechanism of a landslide is complicated, and its occurrence is the result of numerous factors [36,50]. Factors affecting the emergence of a landslide vary with different study areas. Therefore, at present, there is no deﬁnite rule for the selec- tion of landslide inﬂuencing factors [33,51]. According to previous studies [5,44,45,47,52] and data availability, the landslide inﬂuencing factors in the study area are divided into four categories, and 20 factors were selected as the initial factors. These include topo- graphic factors (altitude, slope, aspect, plan curvature, proﬁle curvature, degree of relief, and topographic wetness index (TWI)), geological factors (lithology, seismic intensity, dis- tance from fault zones, and stratigraphy), ecological factors (distance from main rivers, distance from streams, annual rainfall, normalized difference vegetation index (NDVI), land cover, and soil erosion intensity), and factors related to human engineering activities (distance from roads, residential kernel density, and distance from hydropower stations). Land cover data originates from GlobeLand30 (http://www.globallandcover.com/, ac- cessed on 21 April 2021), and the NDVI data originates from Geospatial Data Cloud (http://www.gscloud.cn/, accessed on 7 August 2021). Topographic factors including altitude, plan curvature, proﬁle curvature, slope, aspect, degree of relief, and TWI, were derived from a digital elevation model (DEM) with a 30 m resolution. All other factor data including the DEM were provided by the Sichuan Province Bureau of Surveying, Mapping, and Geoinformation, China. In this study, ArcGIS (version 10.7.1, ESRI, Redlands, CA, USA) software was used to overlay all factor layers with the landslide inventory map and then calculate the dis- tance from roads, rivers, faults, and hydropower stations to each grid. Subsequently, all continuous factors were reclassiﬁed according to previous studies and prior knowledge. The equal interval method was used to classify distance factors (such as rivers and roads, and this method was also applied to annual rainfall due to the availability of data). Speciﬁc factors, including plan curvature, proﬁle curvature, and aspect, were classiﬁed based on the experience provided by previous studies [9,30,53]. Other factors were classiﬁed using the Jenks natural breaks method. Table 1 shows the speciﬁc classiﬁcation of each factor, and Figure 2 shows the reclassiﬁed factor layers. Appl. Sci. 2022, 12, 10196 5 of 28 Table 1. Classiﬁcation of landslide inﬂuencing factors. Category Reclassiﬁcation Factor Data Type Class Attribution Method 1. 734–1000; 2. 1000–1400; 3. 1400–1800; 4. Altitude (m) Continuous Equal interval 1800–2200; 5. 2200–2600; 6. >2600 1. 0–12.58; 2. 12.58–27.06; 3. 27.06–36.79; 4. Slope ( ) Continuous Jenks natural breaks 36.79–44.57; 5. 44.57–52.98; 6. >52.98 1. Flat; 2. North; 3. Northeast; 4. East; 5. Aspect Continuous Expert knowledge Southeast; 6. South; 7. Southwest; 8. West; 9. Northwest Topographic 1. <0.001(Concave); 2. Plan curvature Continuous Expert knowledge 0.001–0.001(Plan); 3. >0.001(Convex); 1. <0.001(Convex); 2. Proﬁle curvature Continuous Expert knowledge 0.001–0.001(Plan); 3. >0.001(Concave); 1. 0–8.92; 2. 8.92–16.52; 3. 16.52–22.97; 4. Degree of relief (m) Continuous Jenks natural breaks 22.97–30.94; 5. 30.94–43.98; 6. >43.98 Topographic Wetness 1. 2.16–4.51; 2. 4.51–5.67; 3. 5.67–7.18; 4. Continuous Jenks natural breaks Index (TWI) 7.18–9.54; 5. >9.54 1. Loose deposits 2. Very soft rock; 3. Soft Lithology Categorical —— rock; 4. Hard rock; 5. Very hard rock Seismic intensity Categorical —— 1. VIII; 2. IX; 3. X; 4. XI 1. 0–500; 2. 500–1000; 3. 1000–1500; 4. Distance from fault Continuous Equal interval 1500–2000; 5. 2000–2500; 6. 2500–3000; 7. Geological zones (m) >3000 1. Quaternary; 2. Neogene; 3. Jurassic; 4. Triassic; 5. Permian; 6. Carboniferous; 7. Stratigraphy Categorical —— Devonian; 8. Silurian; 9. Sinian; 10. Archean 1. 0–200; 2. 200–400; 3. 400–600; 4. Distance from main 600–800; 5. 800–1000; 6. 1000–1200; 7. Continuous Equal interval rivers (m) 1200–1400; 8. 1400–1600; 9. 1600–1800; 10. 1800–2000; 11. >2000 Distance from streams 1. 0–100; 2. 100–200; 3. 200–300; 4. Continuous Equal interval (m) 300–400; 5. 400–500; 6. >500 1. <800; 2. 800–900; 3. 900–1000; 4. Annual rainfall (mm) Continuous Equal interval 1000–1100; 5. >1100 Ecological 1. Farmland; 2. Forestland; 3. Grassland; Land cover Categorical —— 4. Water bodies; 5. Artiﬁcial surface Normalized Difference 1. <0.25; 2. 0.25–0.49; 3. 0.49–0.66; 4. Vegetation Index Continuous Jenks natural breaks 0.66–0.79; 5. >0.79 (NDVI) 1. 11; 2. 12; 3. 13; 4. 14; 5. 15; 6. 16; 7. 31; 8. 32; 9. 33; 10. 34; 11. 35 (Levels 11–16 are Soil erosion intensity Categorical —— hydraulic erosion and levels 31–35 are freeze-thaw erosion) 1. 0–200; 2. 200–400; 3. 400–600; 4. Distance from roads Continuous Equal interval 600–800; 5. 800–1000; 6. 1000–1200; 7. (m) 1200–1400; 8. 1400–1600; 9. >1600 Human Residential kernel 1. 0–1.07; 2. 1.07–3.07; 3. 3.07–5.37; 4. Continuous Jenks natural breaks engineering density 5.37–8.10; 5. 8.10–12.34; 6. >12.34; activities Distance from 1. 0–500; 2. 500–1000; 3. 1000–1500; 4. hydropower stations Continuous Equal interval 1500–2000; 5. 2000–2500; 6. 2500–3000; (m) 7. >3000 Appl. Sci. 2022, 12, x FOR PEER REVIEW 6 of 30 Appl. Sci. 2022, 12, 10196 6 of 28 Figure 2. Cont. Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 30 Appl. Sci. 2022, 12, 10196 7 of 28 Figure Figure 2. 2. Landslide Landslide in inﬂuencing fluencing fa factor ctor layers: layers: (a) ( a a)ltaltitude; itude; (b) (slope; b) slope; (c) a (c spec ) aspect; t; (d) pla (d)nplan curvature; curvatu (er )e; profile curvature; (f) degree of relief; (g) topographic wetness index (TWI); (h) lithology; (i) seismic (e) proﬁle curvature; (f) degree of relief; (g) topographic wetness index (TWI); (h) lithology; (i) seismic intensity; (j) distance from fault zones; (k) stratigraphy; (l) distance from main rivers; (m) distance intensity; (j) distance from fault zones; (k) stratigraphy; (l) distance from main rivers; (m) distance from streams; (n) annual rainfall; (o) normalized difference vegetation index (NDVI); (p) land cover; from streams; (n) annual rainfall; (o) normalized difference vegetation index (NDVI); (p) land cover; (q) soil erosion intensity; (r) distance from roads; (s) residential kernel density; (t) distance from (q) soil erosion intensity; (r) distance from roads; (s) residential kernel density; (t) distance from hydropower stations. hydropower stations. 2.3.1. Topographic Factors 2.3.1. Topographic Factors Altitude is a commonly used factor in landslide susceptibility assessments and plays Altitude is a commonly used factor in landslide susceptibility assessments and plays an important role in landslide occurrence demonstrated by many studies [44,45,47,54]. an important role in landslide occurrence demonstrated by many studies [44,45,47,54]. Environmental conditions (such as vegetation distribution and rainfall) vary with altitude, Environmental conditions (such as vegetation distribution and rainfall) vary with altitude, affecting the occurrence of landslides [30]. affecting the occurrence of landslides [30]. Slope is one of the most direct and important factors affecting slope stability [52]. Slope is one of the most direct and important factors affecting slope stability [52]. With With changing slope degrees, the stress field in the slope also changes, affecting slope changing slope degrees, the stress ﬁeld in the slope also changes, affecting slope stability [9]. stability [9]. In general, the steeper the slope, the greater the chance of failure [55]. In general, the steeper the slope, the greater the chance of failure [55]. Aspect refers to the direction a slope faces, which primarily affects environmental Aspect refers to the direction a slope faces, which primarily affects environmental conditions such as soil moisture, weathering, and topographic vegetation through rainfall, conditions such as soil moisture, weathering, and topographic vegetation through rainfall, wind, and solar radiation, thereby indirectly affecting slope stability [53]. Aspect ranges wind, and solar radiation, thereby indirectly affecting slope stability [53]. Aspect ranges from 0° to 360°, which can be divided into eight basic directions of North, Northeast, East, from 0 to 360 , which can be divided into eight basic directions of North, Northeast, East, Southeast, South, Southwest, West, and Northwest, as well as flat areas. Southeast, South, Southwest, West, and Northwest, as well as ﬂat areas. Plan curvature and profile curvature are two types of curvature commonly used in Plan curvature and proﬁle curvature are two types of curvature commonly used landslide susceptibility studies to reflect the geometric characteristics of slopes. The plan in landslide susceptibility studies to reﬂect the geometric characteristics of slopes. The plan curvature affects the convergence and divergence of ﬂow, while the proﬁle curvature Appl. Sci. 2022, 12, 10196 8 of 28 affects the acceleration and deceleration of ﬂow [9,30,36,41,44]. A positive plan curvature indicates that the slope is sideward convex, while a negative value indicates that the slope is sideward concave, and values around zero represent ﬂat surfaces. On the contrary, positive and negative values of proﬁle curvature indicate upward concave and upward convex respectively [9,33]. The degree of relief refers to the difference between the highest altitude and the lowest altitude in a speciﬁc area and has a regional correlation with landslide occurrence [51,52]. The calculation formula is: R = H H (1) max min where R is the degree of relief of a unit area, H is the altitude of the highest point in the max area, and H is the altitude of the lowest point in the area. min TWI is a physical indicator of the impact of regional topography on the direction and accumulation of runoff ﬂow. This index helps identify rainfall-runoff patterns, po- tential areas with increased soil moisture, and waterlogging areas, as well as quantify the control of topography over basic hydrological processes, which is commonly used in landslide susceptibility assessments [36,44,52,53]. In this study, TWI was calculated with the SAGA-GIS (http://saga-gis.org, accessed on 11 July 2021) software using the following calculation formula: TW I = ln( A /tanb) (2) where A is the slope contributing area, and b is the slope gradient. 2.3.2. Geological Factors Lithology is an important factor affecting slope stability, which is commonly used as a key factor in landslide studies [41]. Changes in lithology largely alter the strength and permeability of rocks, resulting in differences in landslide susceptibility [56]. In this study, lithology primarily refers to rock mass strength. Classiﬁcation criteria are based on the “Engineering Rock Mass Classiﬁcation Standard”, which is one of the national standards (GB50218-2014) of China. Earthquakes are commonly regarded as a direct factor leading to landslides, and many scholars have deﬁned them as a landslide-triggering factor [9,33,44,47]. The Wenchuan earthquake in 2008 triggered a large number of landslides in the study area [57] and indirectly led to changes in its ecological environment [45]. In this study, the seismic intensity of the Wenchuan earthquake was used as an inﬂuencing factor and such data was obtained from the China Earthquake Administration (CEA 2008). Faults are another important factor affecting slope stability. Because tectonic faults reduce the strength of the surrounding rock mass, landslides are likely to occur near faults [53,58]. Active faults usually increase the probability of landslide occurrence [41]. The fault zones in the study area are relatively well-developed, making them prone to geological disasters [45]. Permeability and strength of rocks and soils can vary signiﬁcantly with stratigraphy (divided by geological ages), which is closely related to the change of slope stability [53,59]. According to research [60], stratigraphy has a speciﬁc inﬂuence on the distribution of landslides. In certain stratigraphy, the slope will be more susceptible to sliding. Therefore, some scholars have considered this factor in the study of landslide susceptibility [5,61]. There are 10 types of stratigraphy with different geological ages in the study area. 2.3.3. Ecological Factors Erosion of the slope toe by ﬂuvial activity, changes in pore water pressure, and runoff can lead to a decrease in slope stability [36,41,62]. Therefore, distance from the river is regarded as an important factor causing landslides in the mountains [58]. In general, the smaller the distance to the river, the lower the slope stability, resulting in an increased probability of landslide occurrence [63]. At present, most landslide susceptibility assessment studies have considered the inﬂuence of hydrological networks on landslides. Appl. Sci. 2022, 12, 10196 9 of 28 However, rivers of different scales exert different impacts on slopes, which many studies have ignored, hindering the accurate analysis of the impacts of rivers on landslides. In this study, to accurately identify the relationship between the hydrological network and landslide occurrence, the river system was divided into two categories according to the tributary level: the distance from the main river and the distance from the stream. In this context, the main river refers to tributaries of Grade 6 and above, and the rest are classiﬁed as streams. Rainfall is a major triggering factor for landslides. High-intensity rainfall will lead to an increase in the pore water pressure inside the slope, increasing the sliding mass and decreasing the shear strength of the rock mass, which increases the chance of landslides [9,25]. This study used the annual rainfall in the study area as a landslide influencing factor. Land cover is closely related to the occurrence of landslides [64], as it has a certain impact on the scale and type of landslides [33]. Different land cover types can lead to signiﬁcant differences in vegetation types and frequency of human engineering activities, resulting in changes in landslide susceptibility [41]. NDVI is an index reﬂecting vegetation growth within a given area. Vegetation coverage is closely related to runoff, inﬁltration, and weathering on the slope surfaces [30], affecting the occurrence of landslides. Therefore, NDVI can be used to quantify the impact of vegetation density on landslides [41]. The calculation formula is: N DV I = N I R R N I R + R (3) ( ) ( ) where N I R is the reﬂection value of the near-infrared band, and R is the reﬂection value of the red band. Eroded soil makes up most landslides, reﬂecting the long-term rainfall erosion dam- age of landslides [65]. Soil erosion has a non-negligible effect on the occurrence of land- slides [66]. Soil erosion intensity reﬂects the intensity of destruction, denudation, trans- portation, and deposition of soil in a region under the effect of water, wind, freeze-thaw cycles, or gravity [67]. Soil erosion modulus is the primary index for soil erosion intensity classiﬁcation. The soil erosion intensity classiﬁcation standard in this study is based on the “Classiﬁcation Standard for Soil Erosion Classiﬁcation” (SL 190-2008) issued by the Ministry of Water Resources of China. There are 11 soil erosion intensity levels in the study area, of which levels 11–16 are hydraulic erosion and levels 31–35 are freeze-thaw erosion. 2.3.4. Human Engineering Activity Factors Landslides near highways are a common phenomenon in certain mountainous ar- eas [30,52]. The construction of roads commonly changes the surrounding topography and geological conditions as well as the original equilibrium state of the slope, making it unstable [9,41,56,68,69]. Therefore, the distance from roads is an important human activity factor affecting the occurrence of landslides [25,53,58]. In general, the smaller the distance to roads, the greater the probability of landslides [70]. To quantify the impact of human engineering activities on landslides, different meth- ods (e.g., HAILS and POI kernel density) have been applied to landslide susceptibility studies to represent the intensity of human engineering activities [44,54]. The density of settlements in a speciﬁc area highly reﬂects the strength of human engineering activities in that area. Therefore, residential kernel density was used as an inﬂuencing factor to characterize the intensity of human engineering activities. The study area is rich in water resources, and many water conservancy projects have been constructed, of which hydropower projects are especially common. Reservoir landslide is a typical geological disaster in hydropower reservoirs [71]. Hydropower projects destroy the original ecological environment and change geological conditions. Especially during water storage and drainage, water level ﬂuctuation in the reservoir can destroy the stability of surrounding slopes, leading to landslides [71,72]. Therefore, the distance from hydropower stations was taken as a landslide inﬂuencing factor. Appl. Sci. 2022, 12, 10196 10 of 28 3. Methods 3.1. Statistical Index SI is a binary statistical analysis [33,68]. Because of its simplicity and robustness, SI is commonly used in landslide susceptibility studies [25,69,73,74]. This method objectively assigns weights to each factor class by calculating the natural logarithm of the ratio of the landslide density in a certain factor class to that of the entire study area. The calculation formula of this method is: f L A i j i j i j W = ln = ln (4) i j f L / A where W is the weight value of category j of factor i, f is the landslide density in class j i j i j of factor i, f is the landslide density in the entire study area, L is the number of landslide i j units in class j of factor i, A is the number of units contained in class j of factor i, L is the i j total number of landslide units in the study area, and A is the total number of units in the study area. After all W are calculated, the landslide susceptibility index (LSI) of each evaluation i j unit is calculated using the following formula: LS I = W , where n is the number of factors, and W is the weight value of factor i in the evaluation unit. 3.2. GeoDetector GeoDetector is a statistical method that can detect spatial stratiﬁed heterogeneity and identify the underlying driving force [42,43]. This method was originally applied in the ﬁeld of health risk assessment [42] and has been widely used in various ﬁelds in recent years, including landslide susceptibility assessments because of its powerful factor analysis capabilities [42,44,45,52,54]. The basic assumption of the GeoDetector can be drawn as: if the variable X (factors) has an important impact on the variable Y (landslide or not), the distribution of them should be very similar. GeoDetector includes four detectors: risk detector, factor detector, ecological detector, and interaction detector. This study used the factor detector to screen for inﬂuencing factors. GeoDetector is freely available at http://www.geodetector.org/ (accessed on 8 May 2021). The factor detector can detect the extent to which inﬂuencing factors explain the spatially stratiﬁed heterogeneity of a dependent variable and use the q-value to measure this property [43]. The speciﬁc concept of the q value is: L 2 N s å SSW h=1 h q = 1 = 1 (5) Ns SST where SSW = N s (6) å h h=1 SST = Ns (7) h = 1, 2, 3, . . . , L is the strata; N and N are the number of units in stratum h and the 2 2 whole area, respectively; s and s are the variances of the Y in the stratum h and the whole area, respectively; SSW is the sum of variances within the stratum, and SST is the total variances of the whole area. The range of q value is 0 to 1, where the larger the q value, the stronger the explanatory power of the factor X to the variable Y. In addition, the factor detector can also calculate the statistical signiﬁcance of the q value and express it as a p value. A small p value represents strong statistical signiﬁcance [43]. Appl. Sci. 2022, 12, x FOR PEER REVIEW 11 of 30 ℎ = 1,2,3, … , is the strata; and are the number of units in stratum ℎ and the whole area, respectively; and are the variances of the in the stratum ℎ and the whole area, respectively; is the sum of variances within the stratum, and is the total variances of the whole area. The range of q value is 0 to 1, where the larger the q value, the stronger the explana- tory power of the factor to the variable . In addition, the factor detector can also cal- culate the statistical significance of the q value and express it as a p value. A small p value Appl. Sci. 2022, 12, 10196 11 of 28 represents strong statistical significance [43]. 3.3. Recursive Feature Elimination 3.3. Recursive Feature Elimination RFE is a feature screening method derived from machine learning [75]. RFE is essen- RFE is a feature screening method derived from machine learning [75]. RFE is essen- tially a greedy algorithm based on feature sorting technology. The basic idea is to start tially a greedy algorithm based on feature sorting technology. The basic idea is to start from the original feature set and remove the least relevant features according to the fea- from the original feature set and remove the least relevant features according to the feature ture importance determined by the classifier. After several iterations, multiple feature importance determined by the classiﬁer. After several iterations, multiple feature subsets subsets are obtained, and the optimal subset is selected based on the prediction accuracy are obtained, and the optimal subset is selected based on the prediction accuracy of the of the classifier. The premise of RFE is that the classifier can calculate the feature im- classiﬁer. The premise of RFE is that the classiﬁer can calculate the feature importance portance (such as random forest and support vector machine). (such as random forest and support vector machine). The flowchart of the RFE method is shown in Figure 3, which mainly includes five The ﬂowchart of the RFE method is shown in Figure 3, which mainly includes ﬁve steps. (1) The initial feature set { , , , … , } contains n features, and the classifier is steps. (1) The initial feature set F , F , F , . . . , F contains n features, and the classiﬁer f g 1 2 3 n trained on this basis. (2) The importance ranking of the features in the feature set is calcu- is trained on this basis. (2) The importance ranking of the features in the feature set is lated. (3) The least relevant feature is eliminated according to the importance ranking, and calculated. (3) The least relevant feature is eliminated according to the importance ranking, a new feature subset { , , … , , , … , , } containing − 1 features is ob- and a new feature subset f F , F , . . . , F , F ,. . . ,F , F g containing n 1 features is 1 2 k1 k+1 n1 n tained. (4) The feature subset obtained in Step 3 is taken as a new feature set, and Steps 1– obtained. (4) The feature subset obtained in Step 3 is taken as a new feature set, and Steps 3 are repeated. A new feature subset is obtained in each iteration, and finally, feature 1–3 are repeated. A new feature subset is obtained in each iteration, and ﬁnally, n feature subsets are obtained. (5) According to the accuracy of the classifier, the optimal subset is subsets are obtained. (5) According to the accuracy of the classiﬁer, the optimal subset is selected selected. . Figu Figure re 3. 3. Flo Flow w cha chart rt of the RF of the RFE E algori algorithm. thm. 3.4. Gaussian Process Regression As a kernel-based machine learning algorithm, GPR can effectively analyze small samples and low-dimensional regression problems and is therefore widely used in the research ﬁelds of lithium-ion battery and solar energy prediction [76,77]. GPR is essentially a non-parametric model that uses Gaussian process priors to perform regression analysis on data [78]. GPR uses probabilistic methods to train on sample data, while other regression methods require detailed modeling parameters. Furthermore, GPR is determined by both the mean function and covariance function, and Bayesian inference is used to obtain Appl. Sci. 2022, 12, 10196 12 of 28 hypotheses for posterior probability [79]. GPR has wider applicability for dealing with complicated and nonlinear problems [78]. A Gaussian process is commonly determined by the following functional formula: f (x) GP m(x), k x, x (8) where m(x) = E[ f (x)] (9) 0 0 0 k x, x = E ( f (x) m(x)) f x m x (10) 0 n 0 x, x 2 R are random variables, and m(x) and k(x, x ) are mean function and co- variance function, respectively. Usually, m(x) = 0 to simplify the calculation process [77]. Considering that the observed target value y contains noise, the general model for estab- lishing GPR is: y = f (x) + # (11) where # is noise and # N 0, s . Thus, the prior distribution of the observed value y is: 0 2 y N 0, k x, x + s I (12) where I is an n-dimensional identity matrix. Assuming that the testing dataset X and the training dataset X have the same Gaussian distribution, the joint prior distribution of the observed value y and the predicted value y is: y K(X, X) + s I K(X, X ) N 0, (13) y K(X , X) K(X , X ) where K(X, X) is the covariance matrix of the training dataset, K(X , X ) is the covariance matrix of the testing dataset, and K(X, X ) = K(X , X) is the covariance matrix between the training dataset X and the testing dataset X . Accordingly, the posterior distribution of the predicted value y can be calculated as: y jX, y, X N y , cov(y ) (14) where h i y = K(X , X) K(X, X) + s I Y (15) h i cov(y ) = K(X , X ) K(X , X) K(X, X) + s I K(X, X ) (16) and y and cov(y ) are the mean and covariance of the predicted value y on the testing dataset X , respectively. Choosing the covariance function (i.e., the kernel function) is one of the key factors affecting model performance. As part of the model assumptions, the covariance function describes the correlation between samples [79]. Commonly used covariance functions in- clude the rational quadratic covariance function, exponential covariance function, squared exponential covariance function, and Matérn covariance function. In this study, different covariance functions are compared based on the root mean square error (RMSE), and the exponential covariance function with the smallest RMSE was selected. Its functional formula is: k x , x q = s ex p (17) i j where s is the signal standard deviation, s is the characteristic length scale, and r = f l x x x x is the Euclidean distance between x and x . Using the maximum like- i j i j i j lihood method, the hyperparameter q s , s of the covariance function can be obtained. f l Appl. Sci. 2022, 12, x FOR PEER REVIEW 13 of 30 , = (− ) (17) where is the signal standard deviation, is the characteristic length scale, and = − ( − ) is the Euclidean distance between and . Using the maximum Appl. Sci. 2022, 12, 10196 13 of 28 likelihood method, the hyperparameter ( , ) of the covariance function can be ob- tained. 3.5. Model Validation Method 3.5. Model Validation Method The receiver operating The reccharacteristic eiver operating (ROC) chara curve cteristi is widely c (ROC) used curve for ievaluati s widely ngu model sed for evaluating performance inmo landslide del performa susceptibility nce in land st slide udies suscept [41,44ibility ,56,80]. stud Its ies y-axis [41,44, repr 56,8esents 0]. Its y the -axis represents model sensitivity the (i.e., model the sens trueitivi positive ty (i.erate), ., the true while po the sitive x-axis rate) r, epr whil esents e the 1-speciﬁcity x-axis represe (i.e., nts 1-specificity the false positive (i.erate) ., the f [56 alse positi ]. When ve the rate) ar ea [56under ]. When the a the curve rea under (AUC) the c > 0.5, urve the (AU model C) > 0.is 5, the model is considered to have conside a good red classiﬁcation to have a good ability classifica , and tion thealar bilit ger y, a the nd AUC the lar value, ger the the AU str C onger value, the stronger the classification ability of the model [52,68]. To plot the ROC curve, the LSI was taken as the classiﬁcation ability of the model [52,68]. To plot the ROC curve, the LSI was taken as the x-axis (1-speciﬁcity), the x-axis and (1-specif the cumulative icity), and per the centage cumulative of landslide percenta units ge of was landsl taken ide as units the was taken as the y-axis (the sensitivity). Finally, the cumulative curve was plotted [32]. y-axis (the sensitivity). Finally, the cumulative curve was plotted [32]. 4. Modeling Process and Results 4. Modeling Process and Results The modeling process (see Figure 4) can be divided into the following six stages: The modeling process (see Figure 4) can be divided into the following six stages: (1) (1) According to historical landslides, a landslide inventory map was created and subse- According to historical landslides, a landslide inventory map was created and subse- quently divided into a training dataset (70%) and a test dataset (30%). (2) Twenty initial quently divided into a training dataset (70%) and a test dataset (30%). (2) Twenty initial landslide inﬂuencing factors were selected to construct a spatial database. These factors landslide influencing factors were selected to construct a spatial database. These factors were then overlaid were with then the overla landslide id with invent the landslide ory mapinve and nto reclassiﬁed. ry map and (3) rec The lassified SI method . (3) The SI method was used to assign was weights used to a to ssig each n wei class ghts of to factors each class to obtain of factors the SI to model. obtain the (4) The SI mo factors del. (4) The factors were screened using were scree GeoDetector ned using combined GeoDetecwith tor comb recursive ined wi featur th rec eursive elimination, feature and elimi the nation, and the GD-SI model was GDobtained. -SI model (5) was The obtai weights ned. (5of ) The continuous weights of factors contin wer uous e optimized factors were using optimized using GPR, and the ﬁnal GPR, hybrid and the model final GD-GPR-SI hybrid mode was l GD obtained. -GPR-SI was (6) The obtaperformances ined. (6) The per offormance SI, s of SI, GD-SI, and GD-GPR-SI GD-SI, and GD were comp -GPR ar -SI ed were and compare evaluated, d aand nd ev landslide aluated, and la susceptibility ndslide su maps sceptibility maps were ﬁnally drawn. were finally drawn. Figure 4. Methodological ﬂowchart. Figure 4. Methodological flowchart. 4.1. Implementation of SI The SI model was constructed using the training dataset, and a total of 345 landslides were used to calculate the SI weights. By overlaying factor layers with the landslide inventory map, the relationships between factor classes and landslides were obtained (see Table 2). The deﬁnition implies that when the SI value is greater than 0, the factor class exerts a promoting effect on the occurrence of landslides. In contrast, when the SI value is less than 0, the factor class is not conducive to the occurrence of landslides [81]. As there are no landslides in certain factor classes (for example, the number of landslides is 0 when the land cover is water), for these classes, SI values cannot be calculated from the Appl. Sci. 2022, 12, 10196 14 of 28 formula (4). In this study, the minimum SI value (3.352) was obtained when the altitude is 2200–2600 m, indicating that the probability of landslide occurrence is low in this class. Moreover, if there is no landslide in a factor class, the class is unfavorable for the occurrence of landslides. Therefore, the SI value of factor classes without landslides was set to a value less than the minimum value (namely 3.5) to indicate that these classes are extremely unfavorable for the occurrence of landslides. Table 2. The spatial relationship between landslides and inﬂuencing factors and the results of SI. Percentage of No. of Percentage of No. of Pixels Factor Class Pixels in Landslides Landslides in SI Weight in Domain Domain (%) in Domain Domain (%) 734–1000 54,761 5.35% 19 5.51% 0.03 1000–1400 153,709 15.00% 180 52.17% 1.246 1400–1800 182,586 17.82% 128 37.10% 0.733 Altitude (m) 1800–2200 175,340 17.12% 16 4.64% 1.306 2200–2600 169,561 16.55% 2 0.58% 3.352 >2600 288,498 28.16% 0 0.00% 3.500 0–12.58 52,441 5.12% 1 0.29% 2.871 12.58–27.06 95,938 9.36% 4 1.16% 2.089 27.06–36.79 192,817 18.82% 30 8.70% 0.772 Slope ( ) 36.79–44.57 303,340 29.61% 102 29.57% 0.002 44.57–52.98 265,684 25.93% 144 41.74% 0.476 >52.98 114,235 11.15% 64 18.55% 0.509 Flat 8592 0.84% 0 0.00% 3.500 North 123,018 12.01% 7 2.03% 1.778 Northeast 111,941 10.93% 13 3.77% 1.065 East 138,007 13.47% 67 19.42% 0.366 Aspect Southeast 142,757 13.93% 89 25.80% 0.616 South 122,625 11.97% 48 13.91% 0.15 Southwest 109,604 10.70% 25 7.25% 0.390 West 128,926 12.58% 52 15.07% 0.18 Northwest 138,985 13.57% 44 12.75% 0.062 <0.001 (concave) 462,405 45.14% 186 53.91% 0.178 Plan 0.001–0.001 (plan) 16,518 1.61% 0 0.00% 3.500 curvature >0.001 (convex) 545,532 53.25% 159 46.09% 0.144 <0.001 (convex) 500,096 48.82% 154 44.64% 0.089 Proﬁle 0.001–0.001 (plan) 13,696 1.34% 0 0.00% 3.500 curvature >0.001 (concave) 510,663 49.85% 191 55.36% 0.105 0–8.92 92,811 9.06% 3 0.87% 2.344 8.92–16.52 256,435 25.03% 45 13.04% 0.652 Degree of 16.52–22.97 332,950 32.50% 113 32.75% 0.008 relief (m) 22.97–30.94 228,321 22.29% 122 35.36% 0.462 30.94–43.98 92,147 8.99% 54 15.65% 0.554 >43.98 21,791 2.13% 8 2.32% 0.086 2.16–4.51 287,750 28.09% 75 21.74% 0.256 4.51–5.67 359,830 35.12% 126 36.52% 0.039 5.67–7.18 244,013 23.82% 117 33.91% 0.353 TWI 7.18–9.54 87,380 8.53% 25 7.25% 0.163 >9.54 45,482 4.44% 2 0.58% 2.036 Loose deposits 1360 0.13% 0 0.00% 3.500 Very soft rock 2182 0.21% 0 0.00% 3.500 Lithology Soft rock 207,368 20.24% 80 23.19% 0.136 Hard rock 138,648 13.53% 64 18.55% 0.315 Very hard rock 674,897 65.88% 201 58.26% 0.123 Appl. Sci. 2022, 12, 10196 15 of 28 Table 2. Cont. Percentage of No. of Percentage of No. of Pixels Factor Class Pixels in Landslides Landslides in SI Weight in Domain Domain (%) in Domain Domain (%) VIII 118,077 11.53% 6 1.74% 1.891 Seismic IX 275,212 26.86% 169 48.99% 0.601 intensity X 244,590 23.88% 76 22.03% 0.080 XI 386,576 37.73% 94 27.25% 0.326 0–500 184,628 18.02% 153 44.35% 0.9 500–1000 148,152 14.46% 72 20.87% 0.367 Distance from 1000–1500 114,805 11.21% 25 7.25% 0.436 fault zones 1500–2000 91,087 8.89% 23 6.67% 0.288 (m) 2000–2500 78,608 7.67% 15 4.35% 0.568 2500–3000 63,375 6.19% 19 5.51% 0.116 >3000 343,800 33.56% 38 11.01% 1.114 Quaternary 1356 0.13% 0 0.00% 3.500 Neogene 65,904 6.43% 5 1.45% 1.490 Jurassic 2650 0.26% 0 0.00% 3.500 Triassic 123,997 12.10% 38 11.01% 0.094 Permian 560,698 54.73% 224 64.93% 0.171 Stratigraphy Carboniferous 20,863 2.04% 10 2.90% 0.353 Devonian 19,213 1.88% 16 4.64% 0.905 Silurian 29,235 2.85% 8 2.32% 0.208 Sinian 13,305 1.30% 23 6.67% 1.636 Archean 187,234 18.28% 21 6.09% 1.099 0–200 100,243 9.79% 142 41.16% 1.437 200–400 73,927 7.22% 93 26.96% 1.318 400–600 67,217 6.56% 43 12.46% 0.642 600–800 61,451 6.00% 27 7.83% 0.266 Distance from 800–1000 57,068 5.57% 15 4.35% 0.248 main rivers 1000–1200 54,450 5.32% 4 1.16% 1.523 1200–1400 51,788 5.06% 5 1.45% 1.249 (m) 1400–1600 48,893 4.77% 10 2.90% 0.499 1600–1800 46,201 4.51% 4 1.16% 1.358 1800–2000 43,205 4.22% 2 0.58% 1.984 >2000 420,012 41.00% 0 0.00% 3.500 0–100 186,318 18.19% 40 11.59% 0.450 100–200 146,304 14.28% 84 24.35% 0.534 Distance from 200–300 132,049 12.89% 68 19.71% 0.425 streams (m) 300–400 116,847 11.41% 45 13.04% 0.134 400–500 100,868 9.85% 36 10.43% 0.058 >500 342,069 33.39% 72 20.87% 0.470 <800 125,428 12.24% 60 17.39% 0.351 800–900 293,355 28.64% 79 22.90% 0.224 Annual 900–1000 232,367 22.68% 83 24.06% 0.059 rainfall (mm) 1000–1100 281,346 27.46% 81 23.48% 0.157 >1100 91,959 8.98% 42 12.17% 0.305 Farmland 63,219 6.17% 74 21.45% 1.246 Forestland 891,639 87.04% 271 78.55% 0.103 Grassland 43,812 4.28% 0 0.00% 3.500 Land cover Water bodies 23,847 2.33% 0 0.00% 3.500 Artiﬁcial surface 1938 0.19% 0 0.00% 3.500 <0.25 60,448 5.90% 4 1.16% 1.627 0.25–0.49 72,494 7.08% 40 11.59% 0.494 0.49–0.66 176,990 17.28% 85 24.64% 0.355 NDVI 0.66–0.79 340,106 33.20% 145 42.03% 0.236 >0.79 374,417 36.55% 71 20.58% 0.574 Appl. Sci. 2022, 12, 10196 16 of 28 Table 2. Cont. Percentage of No. of Percentage of No. of Pixels Factor Class Pixels in Landslides Landslides in SI Weight in Domain Domain (%) in Domain Domain (%) 11 726,211 70.89% 173 50.14% 0.346 12 70,452 6.88% 77 22.32% 1.177 13 27,335 2.67% 31 8.99% 1.214 14 20,886 2.04% 33 9.57% 1.546 15 17,127 1.67% 7 2.03% 0.194 Soil erosion 16 19,169 1.87% 24 6.96% 1.313 intensity 31 113,698 11.10% 0 0.00% 3.500 32 1829 0.18% 0 0.00% 3.500 33 5632 0.55% 0 0.00% 3.500 34 19,795 1.93% 0 0.00% 3.500 35 2321 0.23% 0 0.00% 3.500 0–200 120,310 11.74% 136 39.42% 1.211 200–400 74,508 7.27% 110 31.88% 1.478 400–600 60,263 5.88% 40 11.59% 0.679 600–800 52,768 5.15% 28 8.12% 0.455 Distance from 800–1000 46,377 4.53% 15 4.35% 0.040 roads (m) 1000–1200 41,758 4.08% 10 2.90% 0.341 1200–1400 38,641 3.77% 2 0.58% 1.873 1400–1600 35,999 3.51% 4 1.16% 1.109 >1600 553,831 54.06% 0 0.00% 3.500 0–1.07 586,432 57.24% 69 20.00% 1.052 1.07–3.07 132,263 12.91% 60 17.39% 0.298 Residential 3.07–5.37 125,950 12.29% 59 17.10% 0.33 kernel density 5.37–8.10 106,213 10.37% 111 32.17% 1.132 8.10–12.34 50,935 4.97% 37 10.72% 0.769 >12.34 22,662 2.21% 9 2.61% 0.165 0–500 21,405 2.09% 47 13.62% 1.875 500–1000 49,830 4.86% 68 19.71% 1.399 1000–1500 64,863 6.33% 38 11.01% 0.554 Distance from 1500–2000 78,032 7.62% 61 17.68% 0.842 hydropower stations (m) 2000–2500 84,266 8.23% 29 8.41% 0.022 2500–3000 78,937 7.71% 29 8.41% 0.087 >3000 647,122 63.17% 73 21.16% 1.094 4.2. Construction of the GD-SI Model 4.2.1. GeoDetector Result GeoDetector analysis was performed using both the spatially superimposed factor data and the landslide training dataset. In this study, landslide inﬂuencing factors are independent variables, and the classiﬁcation is consistent with Table 1, while the dependent variable is the occurrence of a landslide (in which case a value of 1 is assigned) or no occurrence of a landslide (in which case a value of 0 is assigned), which is a binary variable. Because GeoDetector requires negative samples, random sampling was performed to produce the same amount of non-landslide samples. To reduce contingency and make the analysis results more reliable, 10 times random sampling of non-landslide samples were conducted to obtain the 10 times GeoDetector results. The analysis result is determined by the average q value and p value. The factor detector results are shown in Figure 5. The q value is the index of the factor ’s explanatory power for landslides, and the p value represents the statistical signiﬁcance. Appl. Sci. 2022, 12, x FOR PEER REVIEW 17 of 30 analysis results more reliable, 10 times random sampling of non-landslide samples were conducted to obtain the 10 times GeoDetector results. The analysis result is determined by the average q value and p value. The factor detector results are shown in Figure 5. The Appl. Sci. 2022, 12, 10196 17 of 28 q value is the index of the factor’s explanatory power for landslides, and the p value rep- resents the statistical significance. Figure Figure 5. 5. Factor Factor Detector Detector res results. ults. The results show that the q values for the distance from roads (q = 0.701), distance The results show that the q values for the distance from roads (q = 0.701), distance from main rivers (q = 0.626), and altitude (q = 0.555) are among the top three, indicating from main rivers (q = 0.626), and altitude (q = 0.555) are among the top three, indicating that these factors have the greatest impacts on landslides. The q values for plan curvature that these factors have the greatest impacts on landslides. The q values for plan curvature (q = 0.007) and proﬁle curvature (q = 0.005) are both less than 0.01, indicating that these (q = 0.007) and profile curvature (q = 0.005) are both less than 0.01, indicating that these two factors are not related to landslide occurrence. In addition, these two factors did not two factors are not related to landslide occurrence. In addition, these two factors did not pass the signiﬁcance test (p < 0.05). Therefore, plan curvature and proﬁle curvature were pass the significance test (p < 0.05). Therefore, plan curvature and profile curvature were eliminated, and the remaining 18 factors were retained for further factor screening. eliminated, and the remaining 18 factors were retained for further factor screening. 4.2.2. Factor Screening Based on GD and RFE 4.2.2. Factor Screening Based on GD and RFE This study combined GeoDetector with the concept of RFE to perform factor screening This study combined GeoDetector with the concept of RFE to perform factor screen- for SI models. First, 18 landslide inﬂuencing factors preliminarily screened by GeoDetector ing for SI models. First, 18 landslide influencing factors preliminarily screened by were used as the initial feature set. Then, the GeoDetector q-value ranking was used as GeoDetector were used as the initial feature set. Then, the GeoDetector q-value ranking the feature importance ranking. Subsequently, the least important feature was recursively was used as the feature importance ranking. Subsequently, the least important feature removed, and AUC values of the models under each factor subset were recorded in turn. was recursively removed, and AUC values of the models under each factor subset were The results are shown in Figure 6, which depicts the trend of the AUC values of the model recorded in turn. The results are shown in Figure 6, which depicts the trend of the AUC with the number of factors. The results show that when the number of factors is 18, the values of the model with the number of factors. The results show that when the number model AUC value is the highest. of factors is 18, the model AUC value is the highest. Appl. Sci. 2022, 12, x FOR PEER REVIEW 18 of 30 Appl. Sci. 2022, 12, 10196 18 of 28 Figure 6. The results of recursive feature elimination based on GeoDetector. Figure 6. The results of recursive feature elimination based on GeoDetector. Considering the adaptation between the factor importance ranking based on GeoDe- Considering the adaptation between the factor importance ranking based on tector and the SI model, the concept of the RFE algorithm was improved. If the performance GeoDetector and the SI model, the concept of the RFE algorithm was improved. If the of the model is improved after a certain factor is eliminated in order, it indicates that the performance of the model is improved after a certain factor is eliminated in order, it indi- factor has a negative impact on the model to a great probability. Therefore, if the AUC value cates that the factor has a negative impact on the model to a great probability. Therefore, of the model increases, the related factor will be eliminated, as shown by the yellow line in if the AUC value of the model increases, the related factor will be eliminated, as shown Figure 6. As a result, six factors including annual average rainfall, distance from streams, by the yellow line in Figure 6. As a result, six factors including annual average rainfall, NDVI, seismic intensity, distance from fault zones, and residential kernel density were elim- distance from streams, NDVI, seismic intensity, distance from fault zones, and residential inated. The 12 factors of distance from roads, distance from main rivers, altitude, distance kernel density were eliminated. The 12 factors of distance from roads, distance from main from hydropower stations, soil erosion intensity, stratigraphy, land cover, aspect, slope, rivers, altitude, distance from hydropower stations, soil erosion intensity, stratigraphy, degree of relief, topographic wetness index, and lithology were thus retained. The model land cover, aspect, slope, degree of relief, topographic wetness index, and lithology were obtained after screening the factors by this hybrid method was named the GD-SI model. thus retained. The model obtained after screening the factors by this hybrid method was 4.3. Construction of the GD-GPR-SI Model named the GD-SI model. For the traditional bivariate statistical models, each factor class has the same weight, 4.3. Construction of the GD-GPR-SI Model causing all values in the same class for continuous factors to be weighted equally, which is contrary to Tobler ’s First Law of Geography. To solve this problem, the GPR algorithm was For the traditional bivariate statistical models, each factor class has the same weight, used to optimize the weights obtained by the SI model. causing all values in the same class for continuous factors to be weighted equally, which First, for continuous factors, the following eight factors were included: distance from is contrary to Tobler’s First Law of Geography. To solve this problem, the GPR algorithm roads, distance from main rivers, altitude, distance from hydropower stations, aspect, slope, was used to optimize the weights obtained by the SI model. degree of relief, and TWI. The weight of each factor class obtained by the SI model was First, for continuous factors, the following eight factors were included: distance from used as the weight of the central value of the class. Then, the central value of the class was roads, distance from main rivers, altitude, distance from hydropower stations, aspect, used as the independent variable, its weight value was used as the dependent variable, slope, degree of relief, and TWI. The weight of each factor class obtained by the SI model and GPR was used to perform regression learning, giving the weight of all factor values (as was used as the weight of the central value of the class. Then, the central value of the class shown in Figure 7). For discrete factors, including soil erosion intensity, stratigraphy, land was used as the independent variable, its weight value was used as the dependent varia- cover, and lithology, the weights of the SI model were used as ﬁnal weight values. ble, and GPR was used to perform regression learning, giving the weight of all factor val- ues (as shown in Figure 7). For discrete factors, including soil erosion intensity, stratigra- phy, land cover, and lithology, the weights of the SI model were used as final weight val- ues. Appl. Sci. 2022, 12, x FOR PEER REVIEW 19 of 30 Appl. Sci. 2022, 12 , 10196 19 of 28 Figure 7. The algorithm for optimizing the SI model by Gaussian process regression. Figure 7. The algorithm for optimizing the SI model by Gaussian process regression. MATLAB R2020b software was used to implement GPR. The results of the regression MATLAB R2020b software was used to implement GPR. The results of the regression are presented in Figure 8, which shows that the trends of factor weights change with are presented in Figure 8, which shows that the trends of factor weights change with var- varying factor values. The RMSE values of the models for each factor are listed in Table 3. ying factor values. The RMSE values of the models for each factor are listed in Table 3. Finally, the weights of all factors were accumulated to obtain the LSI of each evaluation Finally, the weights of all factors were accumulated to obtain the LSI of each evaluation unit. This hybrid model was named the GD-GPR-SI model. unit. This hybrid model was named the GD-GPR-SI model. Table 3. Root Mean Squared Error (RMSE) of GPR regression results. Table 3. Root Mean Squared Error (RMSE) of GPR regression results. Factors RMSE Factors RMSE Altitude 3.463 10 −4 Altitude 3.463 × 10 Degree of relief 1.296 10 −4 Degree of relief 1.296 × 10 Slope 1.606 10 −4 Aspect Slope 1.356 10 1.606 × 10 Distance from main rivers 6.249 10 −4 Aspect 1.356 × 10 Distance from roads 6.225 10 −4 Distance from main rivers 6.249 × 10 Distance from hydropower stations 1.361 10 −2 Distance from roads 6.225 × 10 TWI 1.158 10 −2 Distance from hydropower stations 1.361 × 10 −4 TWI 1.158 × 10 4.4. Correlation between Selected Factors and Landslide Through factor screening, 12 landslide inﬂuencing factors were retained. Among them, the distance from roads is the most important factor (q = 0.701), and its SI value is the highest (1.478) when it is 200–400 m, indicating that it is most favorable for the occurrence of landslides in this class. As shown by the GPR regression result (see Figure 8a), the greater the distance from roads, the lower the probability of landslide occurrence. The distance from main rivers (q = 0.626) ranked second in importance with the largest SI value (1.437) at 0–200 m. Similar to distance from roads, the factor weight is approximately inversely proportional to the distance (see Figure 8b). As the third most important factor, altitude (q = 0.555) is most favorable for the occurrence of landslides at 1000–1400 m (SI = 1.246), and no landslides occurred in areas above 2600 m. The importance of distance from hydropower stations is second only to that of altitude (q = 0.36) as a human engineering factor in this study. When it is 0–500 m, the SI value is the largest (1.875), and the larger the distance, the smaller the SI value (see Figure 8d). Aspect (q = 0.099), slope (q = 0.08), degree of relief (q = 0.059), and TWI (q = 0.031) are four topographic factors derived from the digital elevation model, and all have a relatively weak inﬂuence on landslide occurrence (q < 0.1). For Aspect, the probability of landslide is highest in the southeastern direction Appl. Sci. 2022, 12, 10196 20 of 28 (SI = 0.616). With an increasing slope (see Table 2 and Figure 8f), the probability of landslide occurrence gradually increases. When the degrees of relief and TWI are 30.94–43.98 m and 5.67–7.18, SI values are the largest at 0.353 and 0.554, respectively. In addition, for geological factors, the two discrete factors stratigraphy (q = 0.117) and lithology (q = 0.019) were retained. For stratigraphy, results show that in Devonian units, landslides are most likely to occur (SI = 0.905), while for lithology, the probability of landslides is highest in hard rock (SI = 0.315). Finally, for environmental factors, in addition to the distance from main rivers, the two factors of soil erosion intensity (0.272) and land cover (0.111) were retained. For soil erosion intensity, hydraulic erosion level 14 (SI = 1.546) is most likely to cause landslides. For land covers, except for water bodies and artiﬁcial surfaces, forestland (SI = 0.103) is Appl. Sci. 2022, 12, x FOR PEER REVIEW 20 of 30 not conducive to the occurrence of landslides, no landslides have occurred on grassland, and farmland (SI = 1.246) is relatively more favorable for the occurrence of landslides. Figu Figure re 8. 8. Resul Results ts o of f w we eiight ght r re egr gres essio sion usin n using g Ga Gaussian ussian pr proces ocesss r regr egess resion sion algorithm: algorithm(:a ()adistance ) distance from from roads; (b) distance from main rivers; (c) altitude; (d) distance from hydropower stations; (e) roads; (b) distance from main rivers; (c) altitude; (d) distance from hydropower stations; (e) aspect; aspect; (f) slope; (g) degree of relief; (h) TWI. (f) slope; (g) degree of relief; (h) TWI. 4.4. Correlation between Selected Factors and Landslide Through factor screening, 12 landslide influencing factors were retained. Among them, the distance from roads is the most important factor (q = 0.701), and its SI value is the highest (1.478) when it is 200–400 m, indicating that it is most favorable for the occur- rence of landslides in this class. As shown by the GPR regression result (see Figure 8a), the greater the distance from roads, the lower the probability of landslide occurrence. The distance from main rivers (q = 0.626) ranked second in importance with the largest SI value (1.437) at 0–200 m. Similar to distance from roads, the factor weight is approximately in- versely proportional to the distance (see Figure 8b). As the third most important factor, altitude (q = 0.555) is most favorable for the occurrence of landslides at 1000–1400 m (SI = 1.246), and no landslides occurred in areas above 2600 m. The importance of distance from hydropower stations is second only to that of altitude (q = 0.36) as a human engineering factor in this study. When it is 0–500 m, the SI value is the largest (1.875), and the larger Appl. Sci. 2022, 12, x FOR PEER REVIEW 21 of 30 the distance, the smaller the SI value (see Figure 8d). Aspect (q = 0.099), slope (q = 0.08), degree of relief (q = 0.059), and TWI (q = 0.031) are four topographic factors derived from the digital elevation model, and all have a relatively weak influence on landslide occur- rence (q < 0.1). For Aspect, the probability of landslide is highest in the southeastern di- rection (SI = 0.616). With an increasing slope (see Table 2 and Figure 8f), the probability of landslide occurrence gradually increases. When the degrees of relief and TWI are 30.94– 43.98 m and 5.67–7.18, SI values are the largest at 0.353 and 0.554, respectively. In addition, for geological factors, the two discrete factors stratigraphy (q = 0.117) and lithology (q = 0.019) were retained. For stratigraphy, results show that in Devonian units, landslides are most likely to occur (SI = 0.905), while for lithology, the probability of landslides is highest in hard rock (SI = 0.315). Finally, for environmental factors, in addition to the distance from main rivers, the two factors of soil erosion intensity (0.272) and land cover (0.111) were retained. For soil erosion intensity, hydraulic erosion level 14 (SI = 1.546) is most likely to cause landslides. For land covers, except for water bodies and artificial surfaces, forestland (SI = −0.103) is not conducive to the occurrence of landslides, no landslides have occurred on grassland, and farmland (SI = 1.246) is relatively more favorable for the oc- currence of landslides. Appl. Sci. 2022, 12, 10196 21 of 28 4.5. Landslide Susceptibility Mapping After obtaining the LSI of each evaluation unit, ArcGIS 10.7.1 software was used to 4.5. Landslide Susceptibility Mapping draw landslide susceptibility maps. The natural breaks method can identify a classifica- tion tAfter hat maximize obtaining s the thediff LSIere ofnce each betwee evaluation n categories, unit, Ar wh cGIS ich 10.7.1 is widely softwar used e was in lan used dslide to draw susceptib landslide ility mappi susceptibility ng [26,30 maps. ]. In thi The s study, natural the breaks natur method al breaks can metho identify d was a classiﬁcation used to di- that maximizes the difference between categories, which is widely used in landslide sus- vide LSI values into five categories from high to low, representing very high, high, mod- ceptibility erate, low, mapping and very [low 26,30 landslide ]. In this study susceptib , theility natural levels, breaks respe method ctively. was Figur used e 9a to –c divide show LSI the values into ﬁve categories from high to low, representing very high, high, moderate, low, landslide susceptibility maps obtained by the SI model, the GD-SI model, and the GD- and very low landslide susceptibility levels, respectively. Figure 9a–c show the landslide GPR-SI model, respectively. Figure 10 shows the area percentage of each susceptibility susceptibility maps obtained by the SI model, the GD-SI model, and the GD-GPR-SI model, class of models. respectively. Figure 10 shows the area percentage of each susceptibility class of models. Appl. Sci. 2022, 12, x FOR PEER REVIEW 22 of 30 Figure 9. Landslide susceptibility maps: (a) SI model; (b) GD-SI model; (c) GD-GPR-SI model. Figure 9. Landslide susceptibility maps: (a) SI model; (b) GD-SI model; (c) GD-GPR-SI model. Figure 10. Area percentage of different susceptibility classes. Figure 10. Area percentage of different susceptibility classes. Based on the landslide susceptibility maps, high susceptibility areas are approximately Based on the landslide susceptibility maps, high susceptibility areas are approxi- distributed along roads and rivers, which is consistent with the distribution of historical mately distributed along roads and rivers, which is consistent with the distribution of his- landslides. Moreover, most landslides are located in valleys, which are also compatible torical landslides. Moreover, most landslides are located in valleys, which are also com- with the characteristics of landslides in mountainous areas [44,82]. These observations patible with the characteristics of landslides in mountainous areas [44,82]. These observa- indicate that the landslide susceptibility maps obtained by the three models are reasonable tions indicate that the landslide susceptibility maps obtained by the three models are rea- and reliable as well as prove the validity of the factor analysis results of GeoDetector. sonable and reliable as well as prove the validity of the factor analysis results of GeoDetector. 4.6. Validation of Models The performance of SI model, GD-SI model, and GD-GPR-SI model was compared and analyzed based on the ROC curves. The accuracy on the testing dataset reflects the predictive ability of the model, and the ROC curves of three models were plotted based on the testing dataset. Figure 11 shows the prediction rate curves of the SI (AUC = 0.931) model, GD-SI (AUC = 0.936) model, and GD-GPR-SI (AUC = 0.943) model. Results show that all three models have strong predictive capabilities (AUC > 0.93), which corroborates the reliability of the SI model. Moreover, the GD-GPR-SI model has the highest AUC value, followed by the GD-SI model, and finally the SI model. Results highlight the supe- riority of the hybrid model. Therefore, both the factor screening method and the GPR op- timization method proposed in this study improved the performance of the SI model and proved effective. Appl. Sci. 2022, 12, 10196 22 of 28 4.6. Validation of Models The performance of SI model, GD-SI model, and GD-GPR-SI model was compared and analyzed based on the ROC curves. The accuracy on the testing dataset reﬂects the predictive ability of the model, and the ROC curves of three models were plotted based on the testing dataset. Figure 11 shows the prediction rate curves of the SI (AUC = 0.931) model, GD-SI (AUC = 0.936) model, and GD-GPR-SI (AUC = 0.943) model. Results show that all three models have strong predictive capabilities (AUC > 0.93), which corroborates the reliability of the SI model. Moreover, the GD-GPR-SI model has the highest AUC value, followed by the GD-SI model, and ﬁnally the SI model. Results highlight the superiority of the hybrid model. Therefore, both the factor screening method and the GPR Appl. Sci. 2022, 12, x FOR PEER REVIEW 23 of 30 optimization method proposed in this study improved the performance of the SI model and proved effective. Figure 11. ROC curves of different models on the testing dataset. Figure 11. ROC curves of different models on the testing dataset. 5. Discussion 5. Discussion 5.1. The Dominant Factors of Landslides in the Study Area 5.1. The dominant Factors of Landslides in the Study Area The selection of landslide impact factors is one of the key steps of landslide susceptibil- The selection of landslide impact factors is one of the key steps of landslide suscepti- ity assessments. Including uncorrelated factors commonly increases model uncertainty [83]. bility assessments. Including uncorrelated factors commonly increases model uncertainty Various methods have been used to select appropriate landslide inﬂuencing factors, but [83]. Various methods have been used to select appropriate landslide influencing factors, there are no deﬁnite rules or universal methods for how to select the best combination of but there are no definite rules or universal methods for how to select the best combination factors [52]. As a statistical model, GeoDetector can make full use of the spatial information of factors [52]. As a statistical model, GeoDetector can make full use of the spatial infor- included in the data to calculate the degree of explanation of the independent variables mation included in the data to calculate the degree of explanation of the independent var- relative to the dependent variables. Several current studies [44,45,52] set the q value thresh- iables relative to the dependent variables. Several current studies [44,45,52] set the q value old based on empirical knowledge, to eliminate factors below the threshold, which are threshold based on empirical knowledge, to eliminate factors below the threshold, which highly subjective approaches. In addition, adapting GeoDetector to the used landslide are highly subjective approaches. In addition, adapting GeoDetector to the used landslide susceptibility evaluation model should also be considered. To address these problems, the susceptibility evaluation model should also be considered. To address these problems, the GeoDetector method was combined with the concept of RFE to construct a new mixed GeoDetector method was combined with the concept of RFE to construct a new mixed factor screening method that can be applied to statistical models. A previous study [54] factor screening method that can be applied to statistical models. A previous study [54] combined these two methods, applied them to the random forest model, and achieved combined these two methods, applied them to the random forest model, and achieved good results. On this basis, the current study applies a combination of these two methods good results. On this basis, the current study applies a combination of these two methods to the traditional bivariate statistical model (SI). The RFE method could be improved to more effectively combine the GeoDetector with the SI model. The initial factor set contains 20 factors. Through the GeoDetector preliminary screening, two factors (i.e., plan curvature and profile curvature) that fail to pass the sig- nificance test were eliminated. Then, using the hybrid method of GeoDetector and RFE, six factors that negatively impacted the model were eliminated, and 12 factors were ac- cordingly retained. By comparing the AUC of the ROC curves of the original factor set and the optimized factor set on the model, the predictive ability of the model using the retained 12 factors (0.936) was found to be higher than that using 20 factors (0.936) (see Figure 11). The number of factors was decreased and the performance of the model was improved, which proves the effectiveness of factor screening. GeoDetector results (see Figure 5) show that among the 12 factors that were finally selected, distance from roads, distance from main rivers, and altitude are the three factors Appl. Sci. 2022, 12, 10196 23 of 28 to the traditional bivariate statistical model (SI). The RFE method could be improved to more effectively combine the GeoDetector with the SI model. The initial factor set contains 20 factors. Through the GeoDetector preliminary screen- ing, two factors (i.e., plan curvature and proﬁle curvature) that fail to pass the signiﬁcance test were eliminated. Then, using the hybrid method of GeoDetector and RFE, six factors that negatively impacted the model were eliminated, and 12 factors were accordingly retained. By comparing the AUC of the ROC curves of the original factor set and the optimized factor set on the model, the predictive ability of the model using the retained 12 factors (0.936) was found to be higher than that using 20 factors (0.936) (see Figure 11). The number of factors was decreased and the performance of the model was improved, which proves the effectiveness of factor screening. GeoDetector results (see Figure 5) show that among the 12 factors that were ﬁnally selected, distance from roads, distance from main rivers, and altitude are the three factors with the strongest effect on landslide occurrence. Historical landslides (see Figure 1) are generally distributed along both sides of roads and rivers, which is consistent with the results of GeoDetector showing that these two factors largely control the distribution of landslides. In addition, the SI values in Table 2 and the regression results in Figure 8a,b show that with increasing distance from main rivers and roads, the SI weight value generally tends to decrease, and the probability of landslide occurrence also gradually decreases, which is consistent with the results of most studies [30,84]. Furthermore, another conclusion of this study is that the impact of rivers at different scales on landslide occurrence is inconsistent. The hydrological network in the study area was classiﬁed into main rivers and streams according to their level of tributaries. Figure 5 shows that the distance from streams has little correlation to landslide occurrence (q < 0.05), while the distance from main rivers has a higher q value (q = 0.626), which is largely due to the different scour and erosion capacities of rivers of different scales. Therefore, future research should consider this difference. The importance of altitude (q = 0.555) ranks after the distance from main rivers. An altitude ranges between 1000–1400 m (SI = 1.246) is most conducive to the occurrence of landslides, while in high-altitude areas, the probability of landslides is very low. Two studies have reached the same conclusion [28,53]. This was found to be largely due to differences in rock characteristics as well as the intensity of human engineering activities at different altitudes [9,85]. Distance from hydropower stations also has a relatively high q value (0.36), and the regression results (see Figure 8d) show that the larger the distance, the lower the probability of landslides. In addition, for land cover, Table 2 shows that 87.04% of the study area is covered by forestland, but the SI value in this area is negative, indicating that it is not favorable for the occurrence of landslides. In contrast, the probability of landslide occurrence in farmland is the highest (SI = 1.246). These results indicate that human engineering activities exert an important impact on the occurrence of landslides in the study area. Therefore, corresponding measures should be taken to address this risk. 5.2. Advantages of the Hybrid Model Aiming at the unreasonable weight distribution of the traditional bivariate statistical models, in this study, GPR in machine learning was used to optimize the factor weights. More reasonable weight values were obtained, which ﬁnally improved the performance of the landslide susceptibility model. Using GPR, the trend of factor values changing with weights can be intuitively displayed, which helps to better grasp the relationship between factors and landslides. This process is primarily derived from interpolation, which indicates that adjacent regions should have the same characteristics. Improving the accuracy of LSM by combining different models and forming a hy- brid model is a common method. At present, many scholars have combined traditional statistical models and opinion-driven models with machine learning-based algorithms, and the performance of the resulting hybrid models is better than that of the original models [9,25,26,74]. These studies show that hybrid models have good application poten- tial, but the key is how to combine models effectively. Machine learning-based models can Appl. Sci. 2022, 12, 10196 24 of 28 mine useful information from a large volume of data, while statistical models have clear mathematical meanings and are conducive to the analysis of the relationships between factors and landslides. Hybrids of both models have been used. The RF-CF (random forest-certainty factor) model proposed by Chen et al. [25], the FT-IV-RF (fractal theory- information value-random forest model) model proposed by Zhao et al. [86], and the EBF-KLR (evidential belief function- kernel logistic regression) model proposed by Chen et al. [74] are innovative combinations of statistical models and machine learning-based models that have been proven to outperform the single models. In this study, a machine learning-based model was used to obtain the distribution pattern of factor weights based on statistical models. The hybrid model combines the advantages of both models, is straight- forward to interpret, and can mine the potential information of factor weights. Therefore, by integrating models, the advantages of different models can be effectively combined, which provides a promising method for landslide susceptibility assessment. 5.3. Limitations of This Study and Prospects of Future Research Although the proposed methods in this study improved the accuracy of landslide susceptibility assessment to a certain extent, certain limitations remain. First, grid units are most commonly used as evaluation units. However, they do not correlate well with real-world geological environments [87]. Therefore, slope units [12] and terrain units [88] have been used in landslide susceptibility assessment. The existing methods for extracting slope units are complicated, and their effect is not ideal. Thus, these methods are not widely used [29]. In addition, the size of grid units also affects the accuracy of landslide susceptibility assessment [89]. Across different study areas, environmental conditions are quite different, and there is no clear criterion for choosing an optimal grid size [56]. In this study, based on literature and expert knowledge as well as considering the computational cost and the actual conditions of the study area, a grid of 30 m 30 m was selected as the evaluation unit. The selection of the optimal evaluation unit is also a difﬁcult problem that should be addressed in future research. Furthermore, in the process of regressing SI weights using GPR, the SI weight value of a class was assigned to the central value of this class. Although this allocation method has brought good results in this study, it still contains some subjectivity. Therefore, future research should consider more reasonable allocation methods to further improve the accuracy of landslide susceptibility assessments. Moreover, considering the second law of geography, a more reasonable screening of regional risk factors should take into account their spatial local heterogeneous (SLH) associations with landslides, and such SLH-based factor screening methods [90,91] are also worthy of continued research in the future. 6. Conclusions For bivariate statistical models such as SI, the distribution of weights does not conform to the reality of factors, which require improvement. Moreover, the selection of factors has a non-negligible impact on the performance of LSM models. This study proposes a hybrid optimization method for the SI model, with the aim of addressing these problems and improving the accuracy and reliability of LSM. The hybrid approach of GeoDetector and RFE was used for factor screening (the obtained model was named GD-SI). The number of factors decreased from 22 to 12, but the AUC value on the testing dataset increased from 0.931 to 0.936. Results show that the prediction performance of the model was improved, proving the effectiveness and reliability of factor screening. Furthermore, the weights of the GD-SI model were optimized using GPR (the obtained model was named GD-GPR-SI). The GD-GPR-SI (AUC = 0.943) model has a higher AUC value than the GD-SI model (AUC = 0.936) on the testing dataset. Therefore, by optimizing GPR, more reasonable weights were obtained, and the predictive ability of the model was improved. The methods proposed in this study improved the predictive ability of the LSM model, which can be used as a general framework for it. The obtained landslide susceptibility maps Appl. Sci. 2022, 12, 10196 25 of 28 can also provide a decision-making basis for landslide prevention and control. Further consideration should be given to the optimization of evaluation units and improvement of the quality of data for modeling. Author Contributions: Conceptualization, Y.Y.; Data curation, Y.Z.; Formal analysis, F.Z.; Investiga- tion, C.S.; Methodology, C.C.; Software, C.C.; Supervision, C.S.; Validation, F.Z.; Visualization, C.S.; Writing—original draft, C.C.; Writing—review & editing, Y.Y. and C.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant num- ber 42071379, 41701448; Technical development project (Potential pipeline threat event identiﬁcation from the perspective of unmanned aerial vehicle) of East Crude Oil Storage and Transportation of National pipe network group Co., Ltd., grant number GWHT20220021074. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data used in this study are available on request from the corre- sponding author. 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Abstract

applied sciences Article An Optimization of Statistical Index Method Based on Gaussian Process Regression and GeoDetector, for Higher Accurate Landslide Susceptibility Modeling 1 , 2 , 3 1 , 2 , 3 , 3 , 4 5 1 , 2 Cen Cheng , Yang Yang *, Fengcheng Zhong , Chao Song and Yan Zhen State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China School of Geosciences and Technology, Southwest Petroleum University, Chengdu 610500, China Spatial Information Technology and Big Data Mining Research Center, Southwest Petroleum University, Chengdu 610500, China Sichuan Xinyang Anchuang Technology Co., Ltd., Chengdu 610500, China HEOA Group, West China School of Public Health and West China Fourth Hospital, Sichuan University, Chengdu 610044, China * Correspondence: yy_swpu@swpu.edu.cn; Tel.: +86-18681279063 Abstract: Landslide susceptibility assessment is an effective non-engineering landslide prevention at the regional scale. This study aims to improve the accuracy of landslide susceptibility assessment by using an optimized statistical index (SI) method. A landslide inventory containing 493 historical landslides was established, and 20 initial inﬂuencing factors were selected for modeling. First, a combination of GeoDetector and recursive feature elimination was used to eliminate the redundant factors. Then, an optimization method for weights of SI was adopted based on Gaussian process regression (GPR). Finally, the predictive abilities of the original SI model, the SI model with optimized factors (GD-SI), and the SI model with optimized factors and weights (GD-GPR-SI) were compared Citation: Cheng, C.; Yang, Y.; Zhong, and evaluated by the area under the receiver operating characteristic curve (AUC) on the testing F.; Song, C.; Zhen, Y. An Optimization of Statistical Index datasets. The GD-GPR-SI model has the highest AUC value (0.943), and the GD-SI model (0.936) also Method Based on Gaussian Process has a higher value than the SI model (0.931). The results highlight the necessity of factor screening Regression and GeoDetector, for and weight optimization. The factor screening method used in this study can effectively eliminate Higher Accurate Landslide factors that negatively affect the SI model. Furthermore, by optimizing the SI weights through GPR, Susceptibility Modeling. Appl. Sci. more reasonable weights can be obtained for model performance improvement. 2022, 12, 10196. https://doi.org/ 10.3390/app122010196 Keywords: landslide susceptibility; statistical index; Gaussian process regression; GeoDetector; Academic Editor: Fernando Rocha recursive feature elimination Received: 18 August 2022 Accepted: 3 October 2022 Published: 11 October 2022 1. Introduction Publisher’s Note: MDPI stays neutral Landslide is a natural disaster that can be deﬁned as the movement of rock, dirt, with regard to jurisdictional claims in or debris down a slope [1]. Landslides are common around the world and commonly published maps and institutional afﬁl- occur in mountainous areas, posing varying degrees of threat to people’s life and property iations. safety [2]. Froude and Petley [3] conducted a temporal and spatial analysis of the global data set of fatal non-seismic landslides from January 2004 to December 2016. Their data showed that 55,997 people were killed in 4862 different landslide events, with Asia being the major region suffering from landslide disasters. In addition, the number of landslides Copyright: © 2022 by the authors. caused by human activities is increasing. Landslide susceptibility mapping (LSM) is an Licensee MDPI, Basel, Switzerland. effective risk assessment method used for landslide prevention and control. In recent This article is an open access article years, various models have been applied to landslide susceptibility mapping. Improving or distributed under the terms and innovating these models to obtain more accurate mapping is a major difﬁculty in landslide conditions of the Creative Commons susceptibility assessment studies [4]. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ At present, quantitative models applied to landslide susceptibility assessment can 4.0/). be divided into four categories: physical-based models, opinion-driven models, bivariate Appl. Sci. 2022, 12, 10196. https://doi.org/10.3390/app122010196 https://www.mdpi.com/journal/applsci Appl. Sci. 2022, 12, 10196 2 of 28 statistical models, and machine learning-based models [5]. Physical-based models are suitable for local-area scale mapping and analysis and have a strong landslide warning abil- ity [6]. However, because of the large amount of required ﬁeld survey data, the evaluation process is complicated and expensive, making it unsuitable for landslide risk evaluation in large-scale areas [7]. Opinion-driven models such as the analytical hierarchy process [8], step-wise assessment ratio analysis [9], and analytical network process [10] have also been applied in numerous landslide susceptibility studies. In these models, evaluation is based on existing expert knowledge, and the evaluation process does not follow a consistent standard, making quantifying the results difﬁcult. Bivariate statistical models are infor- mation mining methods based on statistics, such as frequency ratio (FR) [11,12], statistical index (SI) [13], certainty factor (CF) [14], and evidence weight [15]. This type of model is straightforward to implement, easy to understand, and has satisfactory prediction perfor- mance. More recently, due to the growing development and maturity of big data mining techniques, machine learning has become a hotspot in the ﬁeld of landslide susceptibility research owing to its powerful data analysis and prediction abilities. In essence, machine learning and multivariate statistical analysis intersect. Further examples including logistic regression (LR) [16,17], random forest [18–20], support vector machine [21,22], artiﬁcial neural network [23,24], and other algorithms, have been applied in landslide susceptibility assessment with advanced prediction performance. In addition to the above models, hybrid methods utilizing multiple model types also achieved excellent performance [25,26]. Statistical models and machine learning-based models are the most widely used quan- titative analysis models. However, both types of models have speciﬁc disadvantages. Although machine learning-based algorithms have high predictive accuracy, their underly- ing rules are complicated and difﬁcult to express intuitively. Hence, they are not conducive to analyzing the relationship between landslides and factors [27,28]. Bivariate statistical models overcome this problem [29,30], but they employ a certain irrationality in the distri- bution of weights, which decreases their predictive accuracy. According to Tobler ’s ﬁrst law of geography, objects that are close to each other in geographical space are also more closely related [31]. For models such as SI and FR, each class has the same weight. For continuous factors such as altitude, this leads to sudden changes in the weights at the boundary of different classes, and similar factor values have completely different weights. In the same class, different factor values have the same weight, which is unreasonable [9,32,33]. Model quality is directly related to the accuracy of its evaluation, but the selection of inﬂuencing factors also affects landslide susceptibility evaluation results [34]. At present, popular factor screening methods include the information gain ratio [35], variance inﬂation factors [36], recursive feature elimination (RFE) [37], rough set [38], principal component analysis [39], Pearson correlation coefﬁcient [40], and Spearman correlation coefﬁcient [41]. In addition, the GeoDetector method proposed by Wang et al., (2010) effectively uses spatial information of data to identify the primary factors affecting a certain phenomenon [42,43]. This has been innovatively applied to landslide susceptibility analysis [44,45]. This study aims to develop a hybrid optimization method for the SI model. This method optimizes the SI weight through GPR, which can avoid the irrationality of the bivariate statistical model mentioned above and improve the accuracy of landslide suscep- tibility assessment. In addition, the integration of GeoDetector and RFE is used to further optimize landslide inﬂuencing factors used for modeling. The area along Duwen highway in Sichuan Province, China, was used as the study area. A landslide inventory was created, and the overall performance of the SI model, SI model with optimized factors (GD-SI), and SI model with optimized factors and weights (GD-GPR-SI) were compared and analyzed. 2. Materials 2.1. Study Area The study area stretches along the Duwen Highway (see Figure 1), located in Sichuan 0 0 0 Province, China. Its geographic coverage is 103 36 E–103 64 E longitude and 30 94 N– 0 2 31 52 N latitude, with an area of 922 km . The Minjiang River, an important branch of the Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 of 30 2. Materials 2.1. Study Area The study area stretches along the Duwen Highway (see Figure 1), located in Sichuan Province, China. Its geographic coverage is 103°36′ E–103°64′ E longitude and 30°94′ N– Appl. Sci. 2022, 12, 10196 3 of 28 31°52′ N latitude, with an area of 922 km . The Minjiang River, an important branch of the upper reaches of the Yangtze River, is the main river in the study area. Many hydropower structures have been built along this river to provide energy for nearby areas. The Duwen upper reaches of the Yangtze River, is the main river in the study area. Many hydropower Highway is built along the basin. In addition, many roads are distributed throughout the structures have been built along this river to provide energy for nearby areas. The Duwen study area. On 12 May 2008, an earthquake with a magnitude of Ms 8.0 occurred in the Highway is built along the basin. In addition, many roads are distributed throughout the study area, leading to a large number of secondary disasters, including a large number of study area. On 12 May 2008, an earthquake with a magnitude of Ms 8.0 occurred in the landslides [46]. study area, leading to a large number of secondary disasters, including a large number of landslides [46]. Figure Figure 1.1.Landslide Landslide inventory inventory map map and and location locatioof n of the the study stud ar y ea: area: (a)(location a) locatio of n Sichuan of SichuPr an ovince Province in China; in Chi( n b a); location (b) location of of the study the stuar dy ea; are (ca ) ; study (c) study area area and a landslide nd landsli inventory de inventmap. ory map. The altitude in the study area varies signiﬁcantly. The lowest altitude is ~734 m, and The altitude in the study area varies significantly. The lowest altitude is ~734 m, and the highest altitude is ~5280 m, providing favorable conditions for landslide formation [47]. the highest altitude is ~5280 m, providing favorable conditions for landslide formation The study area has a continental monsoon climate. The annual rainfall is 800–1300 mm [45]. [47]. The study area has a continental monsoon climate. The annual rainfall is 800–1300 There is a wide range of stratigraphic outcrops in the study area, primarily Triassic in mm [45]. There is a wide range of stratigraphic outcrops in the study area, primarily Tri- age. The area has good vegetation coverage and is primarily covered with forests. Hard assic in age. The area has good vegetation coverage and is primarily covered with forests. rocks are mainly distributed in the north and middle of the study area, while soft rocks are Hard rocks are mainly distributed in the north and middle of the study area, while soft primarily distributed in the southern regions. In addition, the exposed bedrock is primarily rocks are primarily distributed in the southern regions. In addition, the exposed bedrock composed of granite, diorite, limestone, phyllite, sandstone, and granite [48]. is primarily composed of granite, diorite, limestone, phyllite, sandstone, and granite [48]. 2.2. Landslide Inventory An accurate landslide inventory map is the basis for effective landslide susceptibility assessment [35]. Landslide data in this study originates from a 0.5 m resolution multi- band remote sensing image obtained by the Pleiades satellite in 2014. Based on remote sensing image interpretation and ﬁeld investigation veriﬁcation, 493 historical landslides were identiﬁed in the study area. According to the Varnes classiﬁcation system [49], the Appl. Sci. 2022, 12, 10196 4 of 28 landslides in the study area mainly belong to rock fall, and a small part of them belong to debris fall and debris ﬂow. The total landslide area is 15.6 km , accounting for 1.69% of the study area. The average area, maximum area, and minimum area of landslide are 2 2 2 0.032 km , 0.991 km , and 0.00041 km respectively. Roads in the study area are the main infrastructure that suffers from landslide damage, causing enormous economic losses. In this study, the geometric center of the landslide surface is taken as the landslide point. According to the data and prior knowledge, a 30 m 30 m grid was selected as the basic evaluation unit. Consequently, 1,024,455 grids were created for the study area, and 493 landslide points were located in different evaluation units, with a total of 493 landslide units. By random sampling, 70% (345 landslides) of landslides were used as training data for modeling, while the other 30% (148 landslides) were used for testing. A landslide inventory map was established using these data (see Figure 1a). 2.3. Landslide Inﬂuencing Factors The selection of inﬂuencing factors is a key step in landslide susceptibility model- ing [30]. The formation mechanism of a landslide is complicated, and its occurrence is the result of numerous factors [36,50]. Factors affecting the emergence of a landslide vary with different study areas. Therefore, at present, there is no deﬁnite rule for the selec- tion of landslide inﬂuencing factors [33,51]. According to previous studies [5,44,45,47,52] and data availability, the landslide inﬂuencing factors in the study area are divided into four categories, and 20 factors were selected as the initial factors. These include topo- graphic factors (altitude, slope, aspect, plan curvature, proﬁle curvature, degree of relief, and topographic wetness index (TWI)), geological factors (lithology, seismic intensity, dis- tance from fault zones, and stratigraphy), ecological factors (distance from main rivers, distance from streams, annual rainfall, normalized difference vegetation index (NDVI), land cover, and soil erosion intensity), and factors related to human engineering activities (distance from roads, residential kernel density, and distance from hydropower stations). Land cover data originates from GlobeLand30 (http://www.globallandcover.com/, ac- cessed on 21 April 2021), and the NDVI data originates from Geospatial Data Cloud (http://www.gscloud.cn/, accessed on 7 August 2021). Topographic factors including altitude, plan curvature, proﬁle curvature, slope, aspect, degree of relief, and TWI, were derived from a digital elevation model (DEM) with a 30 m resolution. All other factor data including the DEM were provided by the Sichuan Province Bureau of Surveying, Mapping, and Geoinformation, China. In this study, ArcGIS (version 10.7.1, ESRI, Redlands, CA, USA) software was used to overlay all factor layers with the landslide inventory map and then calculate the dis- tance from roads, rivers, faults, and hydropower stations to each grid. Subsequently, all continuous factors were reclassiﬁed according to previous studies and prior knowledge. The equal interval method was used to classify distance factors (such as rivers and roads, and this method was also applied to annual rainfall due to the availability of data). Speciﬁc factors, including plan curvature, proﬁle curvature, and aspect, were classiﬁed based on the experience provided by previous studies [9,30,53]. Other factors were classiﬁed using the Jenks natural breaks method. Table 1 shows the speciﬁc classiﬁcation of each factor, and Figure 2 shows the reclassiﬁed factor layers. Appl. Sci. 2022, 12, 10196 5 of 28 Table 1. Classiﬁcation of landslide inﬂuencing factors. Category Reclassiﬁcation Factor Data Type Class Attribution Method 1. 734–1000; 2. 1000–1400; 3. 1400–1800; 4. Altitude (m) Continuous Equal interval 1800–2200; 5. 2200–2600; 6. >2600 1. 0–12.58; 2. 12.58–27.06; 3. 27.06–36.79; 4. Slope ( ) Continuous Jenks natural breaks 36.79–44.57; 5. 44.57–52.98; 6. >52.98 1. Flat; 2. North; 3. Northeast; 4. East; 5. Aspect Continuous Expert knowledge Southeast; 6. South; 7. Southwest; 8. West; 9. Northwest Topographic 1. <0.001(Concave); 2. Plan curvature Continuous Expert knowledge 0.001–0.001(Plan); 3. >0.001(Convex); 1. <0.001(Convex); 2. Proﬁle curvature Continuous Expert knowledge 0.001–0.001(Plan); 3. >0.001(Concave); 1. 0–8.92; 2. 8.92–16.52; 3. 16.52–22.97; 4. Degree of relief (m) Continuous Jenks natural breaks 22.97–30.94; 5. 30.94–43.98; 6. >43.98 Topographic Wetness 1. 2.16–4.51; 2. 4.51–5.67; 3. 5.67–7.18; 4. Continuous Jenks natural breaks Index (TWI) 7.18–9.54; 5. >9.54 1. Loose deposits 2. Very soft rock; 3. Soft Lithology Categorical —— rock; 4. Hard rock; 5. Very hard rock Seismic intensity Categorical —— 1. VIII; 2. IX; 3. X; 4. XI 1. 0–500; 2. 500–1000; 3. 1000–1500; 4. Distance from fault Continuous Equal interval 1500–2000; 5. 2000–2500; 6. 2500–3000; 7. Geological zones (m) >3000 1. Quaternary; 2. Neogene; 3. Jurassic; 4. Triassic; 5. Permian; 6. Carboniferous; 7. Stratigraphy Categorical —— Devonian; 8. Silurian; 9. Sinian; 10. Archean 1. 0–200; 2. 200–400; 3. 400–600; 4. Distance from main 600–800; 5. 800–1000; 6. 1000–1200; 7. Continuous Equal interval rivers (m) 1200–1400; 8. 1400–1600; 9. 1600–1800; 10. 1800–2000; 11. >2000 Distance from streams 1. 0–100; 2. 100–200; 3. 200–300; 4. Continuous Equal interval (m) 300–400; 5. 400–500; 6. >500 1. <800; 2. 800–900; 3. 900–1000; 4. Annual rainfall (mm) Continuous Equal interval 1000–1100; 5. >1100 Ecological 1. Farmland; 2. Forestland; 3. Grassland; Land cover Categorical —— 4. Water bodies; 5. Artiﬁcial surface Normalized Difference 1. <0.25; 2. 0.25–0.49; 3. 0.49–0.66; 4. Vegetation Index Continuous Jenks natural breaks 0.66–0.79; 5. >0.79 (NDVI) 1. 11; 2. 12; 3. 13; 4. 14; 5. 15; 6. 16; 7. 31; 8. 32; 9. 33; 10. 34; 11. 35 (Levels 11–16 are Soil erosion intensity Categorical —— hydraulic erosion and levels 31–35 are freeze-thaw erosion) 1. 0–200; 2. 200–400; 3. 400–600; 4. Distance from roads Continuous Equal interval 600–800; 5. 800–1000; 6. 1000–1200; 7. (m) 1200–1400; 8. 1400–1600; 9. >1600 Human Residential kernel 1. 0–1.07; 2. 1.07–3.07; 3. 3.07–5.37; 4. Continuous Jenks natural breaks engineering density 5.37–8.10; 5. 8.10–12.34; 6. >12.34; activities Distance from 1. 0–500; 2. 500–1000; 3. 1000–1500; 4. hydropower stations Continuous Equal interval 1500–2000; 5. 2000–2500; 6. 2500–3000; (m) 7. >3000 Appl. Sci. 2022, 12, x FOR PEER REVIEW 6 of 30 Appl. Sci. 2022, 12, 10196 6 of 28 Figure 2. Cont. Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 30 Appl. Sci. 2022, 12, 10196 7 of 28 Figure Figure 2. 2. Landslide Landslide in inﬂuencing fluencing fa factor ctor layers: layers: (a) ( a a)ltaltitude; itude; (b) (slope; b) slope; (c) a (c spec ) aspect; t; (d) pla (d)nplan curvature; curvatu (er )e; profile curvature; (f) degree of relief; (g) topographic wetness index (TWI); (h) lithology; (i) seismic (e) proﬁle curvature; (f) degree of relief; (g) topographic wetness index (TWI); (h) lithology; (i) seismic intensity; (j) distance from fault zones; (k) stratigraphy; (l) distance from main rivers; (m) distance intensity; (j) distance from fault zones; (k) stratigraphy; (l) distance from main rivers; (m) distance from streams; (n) annual rainfall; (o) normalized difference vegetation index (NDVI); (p) land cover; from streams; (n) annual rainfall; (o) normalized difference vegetation index (NDVI); (p) land cover; (q) soil erosion intensity; (r) distance from roads; (s) residential kernel density; (t) distance from (q) soil erosion intensity; (r) distance from roads; (s) residential kernel density; (t) distance from hydropower stations. hydropower stations. 2.3.1. Topographic Factors 2.3.1. Topographic Factors Altitude is a commonly used factor in landslide susceptibility assessments and plays Altitude is a commonly used factor in landslide susceptibility assessments and plays an important role in landslide occurrence demonstrated by many studies [44,45,47,54]. an important role in landslide occurrence demonstrated by many studies [44,45,47,54]. Environmental conditions (such as vegetation distribution and rainfall) vary with altitude, Environmental conditions (such as vegetation distribution and rainfall) vary with altitude, affecting the occurrence of landslides [30]. affecting the occurrence of landslides [30]. Slope is one of the most direct and important factors affecting slope stability [52]. Slope is one of the most direct and important factors affecting slope stability [52]. With With changing slope degrees, the stress field in the slope also changes, affecting slope changing slope degrees, the stress ﬁeld in the slope also changes, affecting slope stability [9]. stability [9]. In general, the steeper the slope, the greater the chance of failure [55]. In general, the steeper the slope, the greater the chance of failure [55]. Aspect refers to the direction a slope faces, which primarily affects environmental Aspect refers to the direction a slope faces, which primarily affects environmental conditions such as soil moisture, weathering, and topographic vegetation through rainfall, conditions such as soil moisture, weathering, and topographic vegetation through rainfall, wind, and solar radiation, thereby indirectly affecting slope stability [53]. Aspect ranges wind, and solar radiation, thereby indirectly affecting slope stability [53]. Aspect ranges from 0° to 360°, which can be divided into eight basic directions of North, Northeast, East, from 0 to 360 , which can be divided into eight basic directions of North, Northeast, East, Southeast, South, Southwest, West, and Northwest, as well as flat areas. Southeast, South, Southwest, West, and Northwest, as well as ﬂat areas. Plan curvature and profile curvature are two types of curvature commonly used in Plan curvature and proﬁle curvature are two types of curvature commonly used landslide susceptibility studies to reflect the geometric characteristics of slopes. The plan in landslide susceptibility studies to reﬂect the geometric characteristics of slopes. The plan curvature affects the convergence and divergence of ﬂow, while the proﬁle curvature Appl. Sci. 2022, 12, 10196 8 of 28 affects the acceleration and deceleration of ﬂow [9,30,36,41,44]. A positive plan curvature indicates that the slope is sideward convex, while a negative value indicates that the slope is sideward concave, and values around zero represent ﬂat surfaces. On the contrary, positive and negative values of proﬁle curvature indicate upward concave and upward convex respectively [9,33]. The degree of relief refers to the difference between the highest altitude and the lowest altitude in a speciﬁc area and has a regional correlation with landslide occurrence [51,52]. The calculation formula is: R = H H (1) max min where R is the degree of relief of a unit area, H is the altitude of the highest point in the max area, and H is the altitude of the lowest point in the area. min TWI is a physical indicator of the impact of regional topography on the direction and accumulation of runoff ﬂow. This index helps identify rainfall-runoff patterns, po- tential areas with increased soil moisture, and waterlogging areas, as well as quantify the control of topography over basic hydrological processes, which is commonly used in landslide susceptibility assessments [36,44,52,53]. In this study, TWI was calculated with the SAGA-GIS (http://saga-gis.org, accessed on 11 July 2021) software using the following calculation formula: TW I = ln( A /tanb) (2) where A is the slope contributing area, and b is the slope gradient. 2.3.2. Geological Factors Lithology is an important factor affecting slope stability, which is commonly used as a key factor in landslide studies [41]. Changes in lithology largely alter the strength and permeability of rocks, resulting in differences in landslide susceptibility [56]. In this study, lithology primarily refers to rock mass strength. Classiﬁcation criteria are based on the “Engineering Rock Mass Classiﬁcation Standard”, which is one of the national standards (GB50218-2014) of China. Earthquakes are commonly regarded as a direct factor leading to landslides, and many scholars have deﬁned them as a landslide-triggering factor [9,33,44,47]. The Wenchuan earthquake in 2008 triggered a large number of landslides in the study area [57] and indirectly led to changes in its ecological environment [45]. In this study, the seismic intensity of the Wenchuan earthquake was used as an inﬂuencing factor and such data was obtained from the China Earthquake Administration (CEA 2008). Faults are another important factor affecting slope stability. Because tectonic faults reduce the strength of the surrounding rock mass, landslides are likely to occur near faults [53,58]. Active faults usually increase the probability of landslide occurrence [41]. The fault zones in the study area are relatively well-developed, making them prone to geological disasters [45]. Permeability and strength of rocks and soils can vary signiﬁcantly with stratigraphy (divided by geological ages), which is closely related to the change of slope stability [53,59]. According to research [60], stratigraphy has a speciﬁc inﬂuence on the distribution of landslides. In certain stratigraphy, the slope will be more susceptible to sliding. Therefore, some scholars have considered this factor in the study of landslide susceptibility [5,61]. There are 10 types of stratigraphy with different geological ages in the study area. 2.3.3. Ecological Factors Erosion of the slope toe by ﬂuvial activity, changes in pore water pressure, and runoff can lead to a decrease in slope stability [36,41,62]. Therefore, distance from the river is regarded as an important factor causing landslides in the mountains [58]. In general, the smaller the distance to the river, the lower the slope stability, resulting in an increased probability of landslide occurrence [63]. At present, most landslide susceptibility assessment studies have considered the inﬂuence of hydrological networks on landslides. Appl. Sci. 2022, 12, 10196 9 of 28 However, rivers of different scales exert different impacts on slopes, which many studies have ignored, hindering the accurate analysis of the impacts of rivers on landslides. In this study, to accurately identify the relationship between the hydrological network and landslide occurrence, the river system was divided into two categories according to the tributary level: the distance from the main river and the distance from the stream. In this context, the main river refers to tributaries of Grade 6 and above, and the rest are classiﬁed as streams. Rainfall is a major triggering factor for landslides. High-intensity rainfall will lead to an increase in the pore water pressure inside the slope, increasing the sliding mass and decreasing the shear strength of the rock mass, which increases the chance of landslides [9,25]. This study used the annual rainfall in the study area as a landslide influencing factor. Land cover is closely related to the occurrence of landslides [64], as it has a certain impact on the scale and type of landslides [33]. Different land cover types can lead to signiﬁcant differences in vegetation types and frequency of human engineering activities, resulting in changes in landslide susceptibility [41]. NDVI is an index reﬂecting vegetation growth within a given area. Vegetation coverage is closely related to runoff, inﬁltration, and weathering on the slope surfaces [30], affecting the occurrence of landslides. Therefore, NDVI can be used to quantify the impact of vegetation density on landslides [41]. The calculation formula is: N DV I = N I R R N I R + R (3) ( ) ( ) where N I R is the reﬂection value of the near-infrared band, and R is the reﬂection value of the red band. Eroded soil makes up most landslides, reﬂecting the long-term rainfall erosion dam- age of landslides [65]. Soil erosion has a non-negligible effect on the occurrence of land- slides [66]. Soil erosion intensity reﬂects the intensity of destruction, denudation, trans- portation, and deposition of soil in a region under the effect of water, wind, freeze-thaw cycles, or gravity [67]. Soil erosion modulus is the primary index for soil erosion intensity classiﬁcation. The soil erosion intensity classiﬁcation standard in this study is based on the “Classiﬁcation Standard for Soil Erosion Classiﬁcation” (SL 190-2008) issued by the Ministry of Water Resources of China. There are 11 soil erosion intensity levels in the study area, of which levels 11–16 are hydraulic erosion and levels 31–35 are freeze-thaw erosion. 2.3.4. Human Engineering Activity Factors Landslides near highways are a common phenomenon in certain mountainous ar- eas [30,52]. The construction of roads commonly changes the surrounding topography and geological conditions as well as the original equilibrium state of the slope, making it unstable [9,41,56,68,69]. Therefore, the distance from roads is an important human activity factor affecting the occurrence of landslides [25,53,58]. In general, the smaller the distance to roads, the greater the probability of landslides [70]. To quantify the impact of human engineering activities on landslides, different meth- ods (e.g., HAILS and POI kernel density) have been applied to landslide susceptibility studies to represent the intensity of human engineering activities [44,54]. The density of settlements in a speciﬁc area highly reﬂects the strength of human engineering activities in that area. Therefore, residential kernel density was used as an inﬂuencing factor to characterize the intensity of human engineering activities. The study area is rich in water resources, and many water conservancy projects have been constructed, of which hydropower projects are especially common. Reservoir landslide is a typical geological disaster in hydropower reservoirs [71]. Hydropower projects destroy the original ecological environment and change geological conditions. Especially during water storage and drainage, water level ﬂuctuation in the reservoir can destroy the stability of surrounding slopes, leading to landslides [71,72]. Therefore, the distance from hydropower stations was taken as a landslide inﬂuencing factor. Appl. Sci. 2022, 12, 10196 10 of 28 3. Methods 3.1. Statistical Index SI is a binary statistical analysis [33,68]. Because of its simplicity and robustness, SI is commonly used in landslide susceptibility studies [25,69,73,74]. This method objectively assigns weights to each factor class by calculating the natural logarithm of the ratio of the landslide density in a certain factor class to that of the entire study area. The calculation formula of this method is: f L A i j i j i j W = ln = ln (4) i j f L / A where W is the weight value of category j of factor i, f is the landslide density in class j i j i j of factor i, f is the landslide density in the entire study area, L is the number of landslide i j units in class j of factor i, A is the number of units contained in class j of factor i, L is the i j total number of landslide units in the study area, and A is the total number of units in the study area. After all W are calculated, the landslide susceptibility index (LSI) of each evaluation i j unit is calculated using the following formula: LS I = W , where n is the number of factors, and W is the weight value of factor i in the evaluation unit. 3.2. GeoDetector GeoDetector is a statistical method that can detect spatial stratiﬁed heterogeneity and identify the underlying driving force [42,43]. This method was originally applied in the ﬁeld of health risk assessment [42] and has been widely used in various ﬁelds in recent years, including landslide susceptibility assessments because of its powerful factor analysis capabilities [42,44,45,52,54]. The basic assumption of the GeoDetector can be drawn as: if the variable X (factors) has an important impact on the variable Y (landslide or not), the distribution of them should be very similar. GeoDetector includes four detectors: risk detector, factor detector, ecological detector, and interaction detector. This study used the factor detector to screen for inﬂuencing factors. GeoDetector is freely available at http://www.geodetector.org/ (accessed on 8 May 2021). The factor detector can detect the extent to which inﬂuencing factors explain the spatially stratiﬁed heterogeneity of a dependent variable and use the q-value to measure this property [43]. The speciﬁc concept of the q value is: L 2 N s å SSW h=1 h q = 1 = 1 (5) Ns SST where SSW = N s (6) å h h=1 SST = Ns (7) h = 1, 2, 3, . . . , L is the strata; N and N are the number of units in stratum h and the 2 2 whole area, respectively; s and s are the variances of the Y in the stratum h and the whole area, respectively; SSW is the sum of variances within the stratum, and SST is the total variances of the whole area. The range of q value is 0 to 1, where the larger the q value, the stronger the explanatory power of the factor X to the variable Y. In addition, the factor detector can also calculate the statistical signiﬁcance of the q value and express it as a p value. A small p value represents strong statistical signiﬁcance [43]. Appl. Sci. 2022, 12, x FOR PEER REVIEW 11 of 30 ℎ = 1,2,3, … , is the strata; and are the number of units in stratum ℎ and the whole area, respectively; and are the variances of the in the stratum ℎ and the whole area, respectively; is the sum of variances within the stratum, and is the total variances of the whole area. The range of q value is 0 to 1, where the larger the q value, the stronger the explana- tory power of the factor to the variable . In addition, the factor detector can also cal- culate the statistical significance of the q value and express it as a p value. A small p value Appl. Sci. 2022, 12, 10196 11 of 28 represents strong statistical significance [43]. 3.3. Recursive Feature Elimination 3.3. Recursive Feature Elimination RFE is a feature screening method derived from machine learning [75]. RFE is essen- RFE is a feature screening method derived from machine learning [75]. RFE is essen- tially a greedy algorithm based on feature sorting technology. The basic idea is to start tially a greedy algorithm based on feature sorting technology. The basic idea is to start from the original feature set and remove the least relevant features according to the fea- from the original feature set and remove the least relevant features according to the feature ture importance determined by the classifier. After several iterations, multiple feature importance determined by the classiﬁer. After several iterations, multiple feature subsets subsets are obtained, and the optimal subset is selected based on the prediction accuracy are obtained, and the optimal subset is selected based on the prediction accuracy of the of the classifier. The premise of RFE is that the classifier can calculate the feature im- classiﬁer. The premise of RFE is that the classiﬁer can calculate the feature importance portance (such as random forest and support vector machine). (such as random forest and support vector machine). The flowchart of the RFE method is shown in Figure 3, which mainly includes five The ﬂowchart of the RFE method is shown in Figure 3, which mainly includes ﬁve steps. (1) The initial feature set { , , , … , } contains n features, and the classifier is steps. (1) The initial feature set F , F , F , . . . , F contains n features, and the classiﬁer f g 1 2 3 n trained on this basis. (2) The importance ranking of the features in the feature set is calcu- is trained on this basis. (2) The importance ranking of the features in the feature set is lated. (3) The least relevant feature is eliminated according to the importance ranking, and calculated. (3) The least relevant feature is eliminated according to the importance ranking, a new feature subset { , , … , , , … , , } containing − 1 features is ob- and a new feature subset f F , F , . . . , F , F ,. . . ,F , F g containing n 1 features is 1 2 k1 k+1 n1 n tained. (4) The feature subset obtained in Step 3 is taken as a new feature set, and Steps 1– obtained. (4) The feature subset obtained in Step 3 is taken as a new feature set, and Steps 3 are repeated. A new feature subset is obtained in each iteration, and finally, feature 1–3 are repeated. A new feature subset is obtained in each iteration, and ﬁnally, n feature subsets are obtained. (5) According to the accuracy of the classifier, the optimal subset is subsets are obtained. (5) According to the accuracy of the classiﬁer, the optimal subset is selected selected. . Figu Figure re 3. 3. Flo Flow w cha chart rt of the RF of the RFE E algori algorithm. thm. 3.4. Gaussian Process Regression As a kernel-based machine learning algorithm, GPR can effectively analyze small samples and low-dimensional regression problems and is therefore widely used in the research ﬁelds of lithium-ion battery and solar energy prediction [76,77]. GPR is essentially a non-parametric model that uses Gaussian process priors to perform regression analysis on data [78]. GPR uses probabilistic methods to train on sample data, while other regression methods require detailed modeling parameters. Furthermore, GPR is determined by both the mean function and covariance function, and Bayesian inference is used to obtain Appl. Sci. 2022, 12, 10196 12 of 28 hypotheses for posterior probability [79]. GPR has wider applicability for dealing with complicated and nonlinear problems [78]. A Gaussian process is commonly determined by the following functional formula: f (x) GP m(x), k x, x (8) where m(x) = E[ f (x)] (9) 0 0 0 k x, x = E ( f (x) m(x)) f x m x (10) 0 n 0 x, x 2 R are random variables, and m(x) and k(x, x ) are mean function and co- variance function, respectively. Usually, m(x) = 0 to simplify the calculation process [77]. Considering that the observed target value y contains noise, the general model for estab- lishing GPR is: y = f (x) + # (11) where # is noise and # N 0, s . Thus, the prior distribution of the observed value y is: 0 2 y N 0, k x, x + s I (12) where I is an n-dimensional identity matrix. Assuming that the testing dataset X and the training dataset X have the same Gaussian distribution, the joint prior distribution of the observed value y and the predicted value y is: y K(X, X) + s I K(X, X ) N 0, (13) y K(X , X) K(X , X ) where K(X, X) is the covariance matrix of the training dataset, K(X , X ) is the covariance matrix of the testing dataset, and K(X, X ) = K(X , X) is the covariance matrix between the training dataset X and the testing dataset X . Accordingly, the posterior distribution of the predicted value y can be calculated as: y jX, y, X N y , cov(y ) (14) where h i y = K(X , X) K(X, X) + s I Y (15) h i cov(y ) = K(X , X ) K(X , X) K(X, X) + s I K(X, X ) (16) and y and cov(y ) are the mean and covariance of the predicted value y on the testing dataset X , respectively. Choosing the covariance function (i.e., the kernel function) is one of the key factors affecting model performance. As part of the model assumptions, the covariance function describes the correlation between samples [79]. Commonly used covariance functions in- clude the rational quadratic covariance function, exponential covariance function, squared exponential covariance function, and Matérn covariance function. In this study, different covariance functions are compared based on the root mean square error (RMSE), and the exponential covariance function with the smallest RMSE was selected. Its functional formula is: k x , x q = s ex p (17) i j where s is the signal standard deviation, s is the characteristic length scale, and r = f l x x x x is the Euclidean distance between x and x . Using the maximum like- i j i j i j lihood method, the hyperparameter q s , s of the covariance function can be obtained. f l Appl. Sci. 2022, 12, x FOR PEER REVIEW 13 of 30 , = (− ) (17) where is the signal standard deviation, is the characteristic length scale, and = − ( − ) is the Euclidean distance between and . Using the maximum Appl. Sci. 2022, 12, 10196 13 of 28 likelihood method, the hyperparameter ( , ) of the covariance function can be ob- tained. 3.5. Model Validation Method 3.5. Model Validation Method The receiver operating The reccharacteristic eiver operating (ROC) chara curve cteristi is widely c (ROC) used curve for ievaluati s widely ngu model sed for evaluating performance inmo landslide del performa susceptibility nce in land st slide udies suscept [41,44ibility ,56,80]. stud Its ies y-axis [41,44, repr 56,8esents 0]. Its y the -axis represents model sensitivity the (i.e., model the sens trueitivi positive ty (i.erate), ., the true while po the sitive x-axis rate) r, epr whil esents e the 1-speciﬁcity x-axis represe (i.e., nts 1-specificity the false positive (i.erate) ., the f [56 alse positi ]. When ve the rate) ar ea [56under ]. When the a the curve rea under (AUC) the c > 0.5, urve the (AU model C) > 0.is 5, the model is considered to have conside a good red classiﬁcation to have a good ability classifica , and tion thealar bilit ger y, a the nd AUC the lar value, ger the the AU str C onger value, the stronger the classification ability of the model [52,68]. To plot the ROC curve, the LSI was taken as the classiﬁcation ability of the model [52,68]. To plot the ROC curve, the LSI was taken as the x-axis (1-speciﬁcity), the x-axis and (1-specif the cumulative icity), and per the centage cumulative of landslide percenta units ge of was landsl taken ide as units the was taken as the y-axis (the sensitivity). Finally, the cumulative curve was plotted [32]. y-axis (the sensitivity). Finally, the cumulative curve was plotted [32]. 4. Modeling Process and Results 4. Modeling Process and Results The modeling process (see Figure 4) can be divided into the following six stages: The modeling process (see Figure 4) can be divided into the following six stages: (1) (1) According to historical landslides, a landslide inventory map was created and subse- According to historical landslides, a landslide inventory map was created and subse- quently divided into a training dataset (70%) and a test dataset (30%). (2) Twenty initial quently divided into a training dataset (70%) and a test dataset (30%). (2) Twenty initial landslide inﬂuencing factors were selected to construct a spatial database. These factors landslide influencing factors were selected to construct a spatial database. These factors were then overlaid were with then the overla landslide id with invent the landslide ory mapinve and nto reclassiﬁed. ry map and (3) rec The lassified SI method . (3) The SI method was used to assign was weights used to a to ssig each n wei class ghts of to factors each class to obtain of factors the SI to model. obtain the (4) The SI mo factors del. (4) The factors were screened using were scree GeoDetector ned using combined GeoDetecwith tor comb recursive ined wi featur th rec eursive elimination, feature and elimi the nation, and the GD-SI model was GDobtained. -SI model (5) was The obtai weights ned. (5of ) The continuous weights of factors contin wer uous e optimized factors were using optimized using GPR, and the ﬁnal GPR, hybrid and the model final GD-GPR-SI hybrid mode was l GD obtained. -GPR-SI was (6) The obtaperformances ined. (6) The per offormance SI, s of SI, GD-SI, and GD-GPR-SI GD-SI, and GD were comp -GPR ar -SI ed were and compare evaluated, d aand nd ev landslide aluated, and la susceptibility ndslide su maps sceptibility maps were ﬁnally drawn. were finally drawn. Figure 4. Methodological ﬂowchart. Figure 4. Methodological flowchart. 4.1. Implementation of SI The SI model was constructed using the training dataset, and a total of 345 landslides were used to calculate the SI weights. By overlaying factor layers with the landslide inventory map, the relationships between factor classes and landslides were obtained (see Table 2). The deﬁnition implies that when the SI value is greater than 0, the factor class exerts a promoting effect on the occurrence of landslides. In contrast, when the SI value is less than 0, the factor class is not conducive to the occurrence of landslides [81]. As there are no landslides in certain factor classes (for example, the number of landslides is 0 when the land cover is water), for these classes, SI values cannot be calculated from the Appl. Sci. 2022, 12, 10196 14 of 28 formula (4). In this study, the minimum SI value (3.352) was obtained when the altitude is 2200–2600 m, indicating that the probability of landslide occurrence is low in this class. Moreover, if there is no landslide in a factor class, the class is unfavorable for the occurrence of landslides. Therefore, the SI value of factor classes without landslides was set to a value less than the minimum value (namely 3.5) to indicate that these classes are extremely unfavorable for the occurrence of landslides. Table 2. The spatial relationship between landslides and inﬂuencing factors and the results of SI. Percentage of No. of Percentage of No. of Pixels Factor Class Pixels in Landslides Landslides in SI Weight in Domain Domain (%) in Domain Domain (%) 734–1000 54,761 5.35% 19 5.51% 0.03 1000–1400 153,709 15.00% 180 52.17% 1.246 1400–1800 182,586 17.82% 128 37.10% 0.733 Altitude (m) 1800–2200 175,340 17.12% 16 4.64% 1.306 2200–2600 169,561 16.55% 2 0.58% 3.352 >2600 288,498 28.16% 0 0.00% 3.500 0–12.58 52,441 5.12% 1 0.29% 2.871 12.58–27.06 95,938 9.36% 4 1.16% 2.089 27.06–36.79 192,817 18.82% 30 8.70% 0.772 Slope ( ) 36.79–44.57 303,340 29.61% 102 29.57% 0.002 44.57–52.98 265,684 25.93% 144 41.74% 0.476 >52.98 114,235 11.15% 64 18.55% 0.509 Flat 8592 0.84% 0 0.00% 3.500 North 123,018 12.01% 7 2.03% 1.778 Northeast 111,941 10.93% 13 3.77% 1.065 East 138,007 13.47% 67 19.42% 0.366 Aspect Southeast 142,757 13.93% 89 25.80% 0.616 South 122,625 11.97% 48 13.91% 0.15 Southwest 109,604 10.70% 25 7.25% 0.390 West 128,926 12.58% 52 15.07% 0.18 Northwest 138,985 13.57% 44 12.75% 0.062 <0.001 (concave) 462,405 45.14% 186 53.91% 0.178 Plan 0.001–0.001 (plan) 16,518 1.61% 0 0.00% 3.500 curvature >0.001 (convex) 545,532 53.25% 159 46.09% 0.144 <0.001 (convex) 500,096 48.82% 154 44.64% 0.089 Proﬁle 0.001–0.001 (plan) 13,696 1.34% 0 0.00% 3.500 curvature >0.001 (concave) 510,663 49.85% 191 55.36% 0.105 0–8.92 92,811 9.06% 3 0.87% 2.344 8.92–16.52 256,435 25.03% 45 13.04% 0.652 Degree of 16.52–22.97 332,950 32.50% 113 32.75% 0.008 relief (m) 22.97–30.94 228,321 22.29% 122 35.36% 0.462 30.94–43.98 92,147 8.99% 54 15.65% 0.554 >43.98 21,791 2.13% 8 2.32% 0.086 2.16–4.51 287,750 28.09% 75 21.74% 0.256 4.51–5.67 359,830 35.12% 126 36.52% 0.039 5.67–7.18 244,013 23.82% 117 33.91% 0.353 TWI 7.18–9.54 87,380 8.53% 25 7.25% 0.163 >9.54 45,482 4.44% 2 0.58% 2.036 Loose deposits 1360 0.13% 0 0.00% 3.500 Very soft rock 2182 0.21% 0 0.00% 3.500 Lithology Soft rock 207,368 20.24% 80 23.19% 0.136 Hard rock 138,648 13.53% 64 18.55% 0.315 Very hard rock 674,897 65.88% 201 58.26% 0.123 Appl. Sci. 2022, 12, 10196 15 of 28 Table 2. Cont. Percentage of No. of Percentage of No. of Pixels Factor Class Pixels in Landslides Landslides in SI Weight in Domain Domain (%) in Domain Domain (%) VIII 118,077 11.53% 6 1.74% 1.891 Seismic IX 275,212 26.86% 169 48.99% 0.601 intensity X 244,590 23.88% 76 22.03% 0.080 XI 386,576 37.73% 94 27.25% 0.326 0–500 184,628 18.02% 153 44.35% 0.9 500–1000 148,152 14.46% 72 20.87% 0.367 Distance from 1000–1500 114,805 11.21% 25 7.25% 0.436 fault zones 1500–2000 91,087 8.89% 23 6.67% 0.288 (m) 2000–2500 78,608 7.67% 15 4.35% 0.568 2500–3000 63,375 6.19% 19 5.51% 0.116 >3000 343,800 33.56% 38 11.01% 1.114 Quaternary 1356 0.13% 0 0.00% 3.500 Neogene 65,904 6.43% 5 1.45% 1.490 Jurassic 2650 0.26% 0 0.00% 3.500 Triassic 123,997 12.10% 38 11.01% 0.094 Permian 560,698 54.73% 224 64.93% 0.171 Stratigraphy Carboniferous 20,863 2.04% 10 2.90% 0.353 Devonian 19,213 1.88% 16 4.64% 0.905 Silurian 29,235 2.85% 8 2.32% 0.208 Sinian 13,305 1.30% 23 6.67% 1.636 Archean 187,234 18.28% 21 6.09% 1.099 0–200 100,243 9.79% 142 41.16% 1.437 200–400 73,927 7.22% 93 26.96% 1.318 400–600 67,217 6.56% 43 12.46% 0.642 600–800 61,451 6.00% 27 7.83% 0.266 Distance from 800–1000 57,068 5.57% 15 4.35% 0.248 main rivers 1000–1200 54,450 5.32% 4 1.16% 1.523 1200–1400 51,788 5.06% 5 1.45% 1.249 (m) 1400–1600 48,893 4.77% 10 2.90% 0.499 1600–1800 46,201 4.51% 4 1.16% 1.358 1800–2000 43,205 4.22% 2 0.58% 1.984 >2000 420,012 41.00% 0 0.00% 3.500 0–100 186,318 18.19% 40 11.59% 0.450 100–200 146,304 14.28% 84 24.35% 0.534 Distance from 200–300 132,049 12.89% 68 19.71% 0.425 streams (m) 300–400 116,847 11.41% 45 13.04% 0.134 400–500 100,868 9.85% 36 10.43% 0.058 >500 342,069 33.39% 72 20.87% 0.470 <800 125,428 12.24% 60 17.39% 0.351 800–900 293,355 28.64% 79 22.90% 0.224 Annual 900–1000 232,367 22.68% 83 24.06% 0.059 rainfall (mm) 1000–1100 281,346 27.46% 81 23.48% 0.157 >1100 91,959 8.98% 42 12.17% 0.305 Farmland 63,219 6.17% 74 21.45% 1.246 Forestland 891,639 87.04% 271 78.55% 0.103 Grassland 43,812 4.28% 0 0.00% 3.500 Land cover Water bodies 23,847 2.33% 0 0.00% 3.500 Artiﬁcial surface 1938 0.19% 0 0.00% 3.500 <0.25 60,448 5.90% 4 1.16% 1.627 0.25–0.49 72,494 7.08% 40 11.59% 0.494 0.49–0.66 176,990 17.28% 85 24.64% 0.355 NDVI 0.66–0.79 340,106 33.20% 145 42.03% 0.236 >0.79 374,417 36.55% 71 20.58% 0.574 Appl. Sci. 2022, 12, 10196 16 of 28 Table 2. Cont. Percentage of No. of Percentage of No. of Pixels Factor Class Pixels in Landslides Landslides in SI Weight in Domain Domain (%) in Domain Domain (%) 11 726,211 70.89% 173 50.14% 0.346 12 70,452 6.88% 77 22.32% 1.177 13 27,335 2.67% 31 8.99% 1.214 14 20,886 2.04% 33 9.57% 1.546 15 17,127 1.67% 7 2.03% 0.194 Soil erosion 16 19,169 1.87% 24 6.96% 1.313 intensity 31 113,698 11.10% 0 0.00% 3.500 32 1829 0.18% 0 0.00% 3.500 33 5632 0.55% 0 0.00% 3.500 34 19,795 1.93% 0 0.00% 3.500 35 2321 0.23% 0 0.00% 3.500 0–200 120,310 11.74% 136 39.42% 1.211 200–400 74,508 7.27% 110 31.88% 1.478 400–600 60,263 5.88% 40 11.59% 0.679 600–800 52,768 5.15% 28 8.12% 0.455 Distance from 800–1000 46,377 4.53% 15 4.35% 0.040 roads (m) 1000–1200 41,758 4.08% 10 2.90% 0.341 1200–1400 38,641 3.77% 2 0.58% 1.873 1400–1600 35,999 3.51% 4 1.16% 1.109 >1600 553,831 54.06% 0 0.00% 3.500 0–1.07 586,432 57.24% 69 20.00% 1.052 1.07–3.07 132,263 12.91% 60 17.39% 0.298 Residential 3.07–5.37 125,950 12.29% 59 17.10% 0.33 kernel density 5.37–8.10 106,213 10.37% 111 32.17% 1.132 8.10–12.34 50,935 4.97% 37 10.72% 0.769 >12.34 22,662 2.21% 9 2.61% 0.165 0–500 21,405 2.09% 47 13.62% 1.875 500–1000 49,830 4.86% 68 19.71% 1.399 1000–1500 64,863 6.33% 38 11.01% 0.554 Distance from 1500–2000 78,032 7.62% 61 17.68% 0.842 hydropower stations (m) 2000–2500 84,266 8.23% 29 8.41% 0.022 2500–3000 78,937 7.71% 29 8.41% 0.087 >3000 647,122 63.17% 73 21.16% 1.094 4.2. Construction of the GD-SI Model 4.2.1. GeoDetector Result GeoDetector analysis was performed using both the spatially superimposed factor data and the landslide training dataset. In this study, landslide inﬂuencing factors are independent variables, and the classiﬁcation is consistent with Table 1, while the dependent variable is the occurrence of a landslide (in which case a value of 1 is assigned) or no occurrence of a landslide (in which case a value of 0 is assigned), which is a binary variable. Because GeoDetector requires negative samples, random sampling was performed to produce the same amount of non-landslide samples. To reduce contingency and make the analysis results more reliable, 10 times random sampling of non-landslide samples were conducted to obtain the 10 times GeoDetector results. The analysis result is determined by the average q value and p value. The factor detector results are shown in Figure 5. The q value is the index of the factor ’s explanatory power for landslides, and the p value represents the statistical signiﬁcance. Appl. Sci. 2022, 12, x FOR PEER REVIEW 17 of 30 analysis results more reliable, 10 times random sampling of non-landslide samples were conducted to obtain the 10 times GeoDetector results. The analysis result is determined by the average q value and p value. The factor detector results are shown in Figure 5. The Appl. Sci. 2022, 12, 10196 17 of 28 q value is the index of the factor’s explanatory power for landslides, and the p value rep- resents the statistical significance. Figure Figure 5. 5. Factor Factor Detector Detector res results. ults. The results show that the q values for the distance from roads (q = 0.701), distance The results show that the q values for the distance from roads (q = 0.701), distance from main rivers (q = 0.626), and altitude (q = 0.555) are among the top three, indicating from main rivers (q = 0.626), and altitude (q = 0.555) are among the top three, indicating that these factors have the greatest impacts on landslides. The q values for plan curvature that these factors have the greatest impacts on landslides. The q values for plan curvature (q = 0.007) and proﬁle curvature (q = 0.005) are both less than 0.01, indicating that these (q = 0.007) and profile curvature (q = 0.005) are both less than 0.01, indicating that these two factors are not related to landslide occurrence. In addition, these two factors did not two factors are not related to landslide occurrence. In addition, these two factors did not pass the signiﬁcance test (p < 0.05). Therefore, plan curvature and proﬁle curvature were pass the significance test (p < 0.05). Therefore, plan curvature and profile curvature were eliminated, and the remaining 18 factors were retained for further factor screening. eliminated, and the remaining 18 factors were retained for further factor screening. 4.2.2. Factor Screening Based on GD and RFE 4.2.2. Factor Screening Based on GD and RFE This study combined GeoDetector with the concept of RFE to perform factor screening This study combined GeoDetector with the concept of RFE to perform factor screen- for SI models. First, 18 landslide inﬂuencing factors preliminarily screened by GeoDetector ing for SI models. First, 18 landslide influencing factors preliminarily screened by were used as the initial feature set. Then, the GeoDetector q-value ranking was used as GeoDetector were used as the initial feature set. Then, the GeoDetector q-value ranking the feature importance ranking. Subsequently, the least important feature was recursively was used as the feature importance ranking. Subsequently, the least important feature removed, and AUC values of the models under each factor subset were recorded in turn. was recursively removed, and AUC values of the models under each factor subset were The results are shown in Figure 6, which depicts the trend of the AUC values of the model recorded in turn. The results are shown in Figure 6, which depicts the trend of the AUC with the number of factors. The results show that when the number of factors is 18, the values of the model with the number of factors. The results show that when the number model AUC value is the highest. of factors is 18, the model AUC value is the highest. Appl. Sci. 2022, 12, x FOR PEER REVIEW 18 of 30 Appl. Sci. 2022, 12, 10196 18 of 28 Figure 6. The results of recursive feature elimination based on GeoDetector. Figure 6. The results of recursive feature elimination based on GeoDetector. Considering the adaptation between the factor importance ranking based on GeoDe- Considering the adaptation between the factor importance ranking based on tector and the SI model, the concept of the RFE algorithm was improved. If the performance GeoDetector and the SI model, the concept of the RFE algorithm was improved. If the of the model is improved after a certain factor is eliminated in order, it indicates that the performance of the model is improved after a certain factor is eliminated in order, it indi- factor has a negative impact on the model to a great probability. Therefore, if the AUC value cates that the factor has a negative impact on the model to a great probability. Therefore, of the model increases, the related factor will be eliminated, as shown by the yellow line in if the AUC value of the model increases, the related factor will be eliminated, as shown Figure 6. As a result, six factors including annual average rainfall, distance from streams, by the yellow line in Figure 6. As a result, six factors including annual average rainfall, NDVI, seismic intensity, distance from fault zones, and residential kernel density were elim- distance from streams, NDVI, seismic intensity, distance from fault zones, and residential inated. The 12 factors of distance from roads, distance from main rivers, altitude, distance kernel density were eliminated. The 12 factors of distance from roads, distance from main from hydropower stations, soil erosion intensity, stratigraphy, land cover, aspect, slope, rivers, altitude, distance from hydropower stations, soil erosion intensity, stratigraphy, degree of relief, topographic wetness index, and lithology were thus retained. The model land cover, aspect, slope, degree of relief, topographic wetness index, and lithology were obtained after screening the factors by this hybrid method was named the GD-SI model. thus retained. The model obtained after screening the factors by this hybrid method was 4.3. Construction of the GD-GPR-SI Model named the GD-SI model. For the traditional bivariate statistical models, each factor class has the same weight, 4.3. Construction of the GD-GPR-SI Model causing all values in the same class for continuous factors to be weighted equally, which is contrary to Tobler ’s First Law of Geography. To solve this problem, the GPR algorithm was For the traditional bivariate statistical models, each factor class has the same weight, used to optimize the weights obtained by the SI model. causing all values in the same class for continuous factors to be weighted equally, which First, for continuous factors, the following eight factors were included: distance from is contrary to Tobler’s First Law of Geography. To solve this problem, the GPR algorithm roads, distance from main rivers, altitude, distance from hydropower stations, aspect, slope, was used to optimize the weights obtained by the SI model. degree of relief, and TWI. The weight of each factor class obtained by the SI model was First, for continuous factors, the following eight factors were included: distance from used as the weight of the central value of the class. Then, the central value of the class was roads, distance from main rivers, altitude, distance from hydropower stations, aspect, used as the independent variable, its weight value was used as the dependent variable, slope, degree of relief, and TWI. The weight of each factor class obtained by the SI model and GPR was used to perform regression learning, giving the weight of all factor values (as was used as the weight of the central value of the class. Then, the central value of the class shown in Figure 7). For discrete factors, including soil erosion intensity, stratigraphy, land was used as the independent variable, its weight value was used as the dependent varia- cover, and lithology, the weights of the SI model were used as ﬁnal weight values. ble, and GPR was used to perform regression learning, giving the weight of all factor val- ues (as shown in Figure 7). For discrete factors, including soil erosion intensity, stratigra- phy, land cover, and lithology, the weights of the SI model were used as final weight val- ues. Appl. Sci. 2022, 12, x FOR PEER REVIEW 19 of 30 Appl. Sci. 2022, 12 , 10196 19 of 28 Figure 7. The algorithm for optimizing the SI model by Gaussian process regression. Figure 7. The algorithm for optimizing the SI model by Gaussian process regression. MATLAB R2020b software was used to implement GPR. The results of the regression MATLAB R2020b software was used to implement GPR. The results of the regression are presented in Figure 8, which shows that the trends of factor weights change with are presented in Figure 8, which shows that the trends of factor weights change with var- varying factor values. The RMSE values of the models for each factor are listed in Table 3. ying factor values. The RMSE values of the models for each factor are listed in Table 3. Finally, the weights of all factors were accumulated to obtain the LSI of each evaluation Finally, the weights of all factors were accumulated to obtain the LSI of each evaluation unit. This hybrid model was named the GD-GPR-SI model. unit. This hybrid model was named the GD-GPR-SI model. Table 3. Root Mean Squared Error (RMSE) of GPR regression results. Table 3. Root Mean Squared Error (RMSE) of GPR regression results. Factors RMSE Factors RMSE Altitude 3.463 10 −4 Altitude 3.463 × 10 Degree of relief 1.296 10 −4 Degree of relief 1.296 × 10 Slope 1.606 10 −4 Aspect Slope 1.356 10 1.606 × 10 Distance from main rivers 6.249 10 −4 Aspect 1.356 × 10 Distance from roads 6.225 10 −4 Distance from main rivers 6.249 × 10 Distance from hydropower stations 1.361 10 −2 Distance from roads 6.225 × 10 TWI 1.158 10 −2 Distance from hydropower stations 1.361 × 10 −4 TWI 1.158 × 10 4.4. Correlation between Selected Factors and Landslide Through factor screening, 12 landslide inﬂuencing factors were retained. Among them, the distance from roads is the most important factor (q = 0.701), and its SI value is the highest (1.478) when it is 200–400 m, indicating that it is most favorable for the occurrence of landslides in this class. As shown by the GPR regression result (see Figure 8a), the greater the distance from roads, the lower the probability of landslide occurrence. The distance from main rivers (q = 0.626) ranked second in importance with the largest SI value (1.437) at 0–200 m. Similar to distance from roads, the factor weight is approximately inversely proportional to the distance (see Figure 8b). As the third most important factor, altitude (q = 0.555) is most favorable for the occurrence of landslides at 1000–1400 m (SI = 1.246), and no landslides occurred in areas above 2600 m. The importance of distance from hydropower stations is second only to that of altitude (q = 0.36) as a human engineering factor in this study. When it is 0–500 m, the SI value is the largest (1.875), and the larger the distance, the smaller the SI value (see Figure 8d). Aspect (q = 0.099), slope (q = 0.08), degree of relief (q = 0.059), and TWI (q = 0.031) are four topographic factors derived from the digital elevation model, and all have a relatively weak inﬂuence on landslide occurrence (q < 0.1). For Aspect, the probability of landslide is highest in the southeastern direction Appl. Sci. 2022, 12, 10196 20 of 28 (SI = 0.616). With an increasing slope (see Table 2 and Figure 8f), the probability of landslide occurrence gradually increases. When the degrees of relief and TWI are 30.94–43.98 m and 5.67–7.18, SI values are the largest at 0.353 and 0.554, respectively. In addition, for geological factors, the two discrete factors stratigraphy (q = 0.117) and lithology (q = 0.019) were retained. For stratigraphy, results show that in Devonian units, landslides are most likely to occur (SI = 0.905), while for lithology, the probability of landslides is highest in hard rock (SI = 0.315). Finally, for environmental factors, in addition to the distance from main rivers, the two factors of soil erosion intensity (0.272) and land cover (0.111) were retained. For soil erosion intensity, hydraulic erosion level 14 (SI = 1.546) is most likely to cause landslides. For land covers, except for water bodies and artiﬁcial surfaces, forestland (SI = 0.103) is Appl. Sci. 2022, 12, x FOR PEER REVIEW 20 of 30 not conducive to the occurrence of landslides, no landslides have occurred on grassland, and farmland (SI = 1.246) is relatively more favorable for the occurrence of landslides. Figu Figure re 8. 8. Resul Results ts o of f w we eiight ght r re egr gres essio sion usin n using g Ga Gaussian ussian pr proces ocesss r regr egess resion sion algorithm: algorithm(:a ()adistance ) distance from from roads; (b) distance from main rivers; (c) altitude; (d) distance from hydropower stations; (e) roads; (b) distance from main rivers; (c) altitude; (d) distance from hydropower stations; (e) aspect; aspect; (f) slope; (g) degree of relief; (h) TWI. (f) slope; (g) degree of relief; (h) TWI. 4.4. Correlation between Selected Factors and Landslide Through factor screening, 12 landslide influencing factors were retained. Among them, the distance from roads is the most important factor (q = 0.701), and its SI value is the highest (1.478) when it is 200–400 m, indicating that it is most favorable for the occur- rence of landslides in this class. As shown by the GPR regression result (see Figure 8a), the greater the distance from roads, the lower the probability of landslide occurrence. The distance from main rivers (q = 0.626) ranked second in importance with the largest SI value (1.437) at 0–200 m. Similar to distance from roads, the factor weight is approximately in- versely proportional to the distance (see Figure 8b). As the third most important factor, altitude (q = 0.555) is most favorable for the occurrence of landslides at 1000–1400 m (SI = 1.246), and no landslides occurred in areas above 2600 m. The importance of distance from hydropower stations is second only to that of altitude (q = 0.36) as a human engineering factor in this study. When it is 0–500 m, the SI value is the largest (1.875), and the larger Appl. Sci. 2022, 12, x FOR PEER REVIEW 21 of 30 the distance, the smaller the SI value (see Figure 8d). Aspect (q = 0.099), slope (q = 0.08), degree of relief (q = 0.059), and TWI (q = 0.031) are four topographic factors derived from the digital elevation model, and all have a relatively weak influence on landslide occur- rence (q < 0.1). For Aspect, the probability of landslide is highest in the southeastern di- rection (SI = 0.616). With an increasing slope (see Table 2 and Figure 8f), the probability of landslide occurrence gradually increases. When the degrees of relief and TWI are 30.94– 43.98 m and 5.67–7.18, SI values are the largest at 0.353 and 0.554, respectively. In addition, for geological factors, the two discrete factors stratigraphy (q = 0.117) and lithology (q = 0.019) were retained. For stratigraphy, results show that in Devonian units, landslides are most likely to occur (SI = 0.905), while for lithology, the probability of landslides is highest in hard rock (SI = 0.315). Finally, for environmental factors, in addition to the distance from main rivers, the two factors of soil erosion intensity (0.272) and land cover (0.111) were retained. For soil erosion intensity, hydraulic erosion level 14 (SI = 1.546) is most likely to cause landslides. For land covers, except for water bodies and artificial surfaces, forestland (SI = −0.103) is not conducive to the occurrence of landslides, no landslides have occurred on grassland, and farmland (SI = 1.246) is relatively more favorable for the oc- currence of landslides. Appl. Sci. 2022, 12, 10196 21 of 28 4.5. Landslide Susceptibility Mapping After obtaining the LSI of each evaluation unit, ArcGIS 10.7.1 software was used to 4.5. Landslide Susceptibility Mapping draw landslide susceptibility maps. The natural breaks method can identify a classifica- tion tAfter hat maximize obtaining s the thediff LSIere ofnce each betwee evaluation n categories, unit, Ar wh cGIS ich 10.7.1 is widely softwar used e was in lan used dslide to draw susceptib landslide ility mappi susceptibility ng [26,30 maps. ]. In thi The s study, natural the breaks natur method al breaks can metho identify d was a classiﬁcation used to di- that maximizes the difference between categories, which is widely used in landslide sus- vide LSI values into five categories from high to low, representing very high, high, mod- ceptibility erate, low, mapping and very [low 26,30 landslide ]. In this study susceptib , theility natural levels, breaks respe method ctively. was Figur used e 9a to –c divide show LSI the values into ﬁve categories from high to low, representing very high, high, moderate, low, landslide susceptibility maps obtained by the SI model, the GD-SI model, and the GD- and very low landslide susceptibility levels, respectively. Figure 9a–c show the landslide GPR-SI model, respectively. Figure 10 shows the area percentage of each susceptibility susceptibility maps obtained by the SI model, the GD-SI model, and the GD-GPR-SI model, class of models. respectively. Figure 10 shows the area percentage of each susceptibility class of models. Appl. Sci. 2022, 12, x FOR PEER REVIEW 22 of 30 Figure 9. Landslide susceptibility maps: (a) SI model; (b) GD-SI model; (c) GD-GPR-SI model. Figure 9. Landslide susceptibility maps: (a) SI model; (b) GD-SI model; (c) GD-GPR-SI model. Figure 10. Area percentage of different susceptibility classes. Figure 10. Area percentage of different susceptibility classes. Based on the landslide susceptibility maps, high susceptibility areas are approximately Based on the landslide susceptibility maps, high susceptibility areas are approxi- distributed along roads and rivers, which is consistent with the distribution of historical mately distributed along roads and rivers, which is consistent with the distribution of his- landslides. Moreover, most landslides are located in valleys, which are also compatible torical landslides. Moreover, most landslides are located in valleys, which are also com- with the characteristics of landslides in mountainous areas [44,82]. These observations patible with the characteristics of landslides in mountainous areas [44,82]. These observa- indicate that the landslide susceptibility maps obtained by the three models are reasonable tions indicate that the landslide susceptibility maps obtained by the three models are rea- and reliable as well as prove the validity of the factor analysis results of GeoDetector. sonable and reliable as well as prove the validity of the factor analysis results of GeoDetector. 4.6. Validation of Models The performance of SI model, GD-SI model, and GD-GPR-SI model was compared and analyzed based on the ROC curves. The accuracy on the testing dataset reflects the predictive ability of the model, and the ROC curves of three models were plotted based on the testing dataset. Figure 11 shows the prediction rate curves of the SI (AUC = 0.931) model, GD-SI (AUC = 0.936) model, and GD-GPR-SI (AUC = 0.943) model. Results show that all three models have strong predictive capabilities (AUC > 0.93), which corroborates the reliability of the SI model. Moreover, the GD-GPR-SI model has the highest AUC value, followed by the GD-SI model, and finally the SI model. Results highlight the supe- riority of the hybrid model. Therefore, both the factor screening method and the GPR op- timization method proposed in this study improved the performance of the SI model and proved effective. Appl. Sci. 2022, 12, 10196 22 of 28 4.6. Validation of Models The performance of SI model, GD-SI model, and GD-GPR-SI model was compared and analyzed based on the ROC curves. The accuracy on the testing dataset reﬂects the predictive ability of the model, and the ROC curves of three models were plotted based on the testing dataset. Figure 11 shows the prediction rate curves of the SI (AUC = 0.931) model, GD-SI (AUC = 0.936) model, and GD-GPR-SI (AUC = 0.943) model. Results show that all three models have strong predictive capabilities (AUC > 0.93), which corroborates the reliability of the SI model. Moreover, the GD-GPR-SI model has the highest AUC value, followed by the GD-SI model, and ﬁnally the SI model. Results highlight the superiority of the hybrid model. Therefore, both the factor screening method and the GPR Appl. Sci. 2022, 12, x FOR PEER REVIEW 23 of 30 optimization method proposed in this study improved the performance of the SI model and proved effective. Figure 11. ROC curves of different models on the testing dataset. Figure 11. ROC curves of different models on the testing dataset. 5. Discussion 5. Discussion 5.1. The Dominant Factors of Landslides in the Study Area 5.1. The dominant Factors of Landslides in the Study Area The selection of landslide impact factors is one of the key steps of landslide susceptibil- The selection of landslide impact factors is one of the key steps of landslide suscepti- ity assessments. Including uncorrelated factors commonly increases model uncertainty [83]. bility assessments. Including uncorrelated factors commonly increases model uncertainty Various methods have been used to select appropriate landslide inﬂuencing factors, but [83]. Various methods have been used to select appropriate landslide influencing factors, there are no deﬁnite rules or universal methods for how to select the best combination of but there are no definite rules or universal methods for how to select the best combination factors [52]. As a statistical model, GeoDetector can make full use of the spatial information of factors [52]. As a statistical model, GeoDetector can make full use of the spatial infor- included in the data to calculate the degree of explanation of the independent variables mation included in the data to calculate the degree of explanation of the independent var- relative to the dependent variables. Several current studies [44,45,52] set the q value thresh- iables relative to the dependent variables. Several current studies [44,45,52] set the q value old based on empirical knowledge, to eliminate factors below the threshold, which are threshold based on empirical knowledge, to eliminate factors below the threshold, which highly subjective approaches. In addition, adapting GeoDetector to the used landslide are highly subjective approaches. In addition, adapting GeoDetector to the used landslide susceptibility evaluation model should also be considered. To address these problems, the susceptibility evaluation model should also be considered. To address these problems, the GeoDetector method was combined with the concept of RFE to construct a new mixed GeoDetector method was combined with the concept of RFE to construct a new mixed factor screening method that can be applied to statistical models. A previous study [54] factor screening method that can be applied to statistical models. A previous study [54] combined these two methods, applied them to the random forest model, and achieved combined these two methods, applied them to the random forest model, and achieved good results. On this basis, the current study applies a combination of these two methods good results. On this basis, the current study applies a combination of these two methods to the traditional bivariate statistical model (SI). The RFE method could be improved to more effectively combine the GeoDetector with the SI model. The initial factor set contains 20 factors. Through the GeoDetector preliminary screening, two factors (i.e., plan curvature and profile curvature) that fail to pass the sig- nificance test were eliminated. Then, using the hybrid method of GeoDetector and RFE, six factors that negatively impacted the model were eliminated, and 12 factors were ac- cordingly retained. By comparing the AUC of the ROC curves of the original factor set and the optimized factor set on the model, the predictive ability of the model using the retained 12 factors (0.936) was found to be higher than that using 20 factors (0.936) (see Figure 11). The number of factors was decreased and the performance of the model was improved, which proves the effectiveness of factor screening. GeoDetector results (see Figure 5) show that among the 12 factors that were finally selected, distance from roads, distance from main rivers, and altitude are the three factors Appl. Sci. 2022, 12, 10196 23 of 28 to the traditional bivariate statistical model (SI). The RFE method could be improved to more effectively combine the GeoDetector with the SI model. The initial factor set contains 20 factors. Through the GeoDetector preliminary screen- ing, two factors (i.e., plan curvature and proﬁle curvature) that fail to pass the signiﬁcance test were eliminated. Then, using the hybrid method of GeoDetector and RFE, six factors that negatively impacted the model were eliminated, and 12 factors were accordingly retained. By comparing the AUC of the ROC curves of the original factor set and the optimized factor set on the model, the predictive ability of the model using the retained 12 factors (0.936) was found to be higher than that using 20 factors (0.936) (see Figure 11). The number of factors was decreased and the performance of the model was improved, which proves the effectiveness of factor screening. GeoDetector results (see Figure 5) show that among the 12 factors that were ﬁnally selected, distance from roads, distance from main rivers, and altitude are the three factors with the strongest effect on landslide occurrence. Historical landslides (see Figure 1) are generally distributed along both sides of roads and rivers, which is consistent with the results of GeoDetector showing that these two factors largely control the distribution of landslides. In addition, the SI values in Table 2 and the regression results in Figure 8a,b show that with increasing distance from main rivers and roads, the SI weight value generally tends to decrease, and the probability of landslide occurrence also gradually decreases, which is consistent with the results of most studies [30,84]. Furthermore, another conclusion of this study is that the impact of rivers at different scales on landslide occurrence is inconsistent. The hydrological network in the study area was classiﬁed into main rivers and streams according to their level of tributaries. Figure 5 shows that the distance from streams has little correlation to landslide occurrence (q < 0.05), while the distance from main rivers has a higher q value (q = 0.626), which is largely due to the different scour and erosion capacities of rivers of different scales. Therefore, future research should consider this difference. The importance of altitude (q = 0.555) ranks after the distance from main rivers. An altitude ranges between 1000–1400 m (SI = 1.246) is most conducive to the occurrence of landslides, while in high-altitude areas, the probability of landslides is very low. Two studies have reached the same conclusion [28,53]. This was found to be largely due to differences in rock characteristics as well as the intensity of human engineering activities at different altitudes [9,85]. Distance from hydropower stations also has a relatively high q value (0.36), and the regression results (see Figure 8d) show that the larger the distance, the lower the probability of landslides. In addition, for land cover, Table 2 shows that 87.04% of the study area is covered by forestland, but the SI value in this area is negative, indicating that it is not favorable for the occurrence of landslides. In contrast, the probability of landslide occurrence in farmland is the highest (SI = 1.246). These results indicate that human engineering activities exert an important impact on the occurrence of landslides in the study area. Therefore, corresponding measures should be taken to address this risk. 5.2. Advantages of the Hybrid Model Aiming at the unreasonable weight distribution of the traditional bivariate statistical models, in this study, GPR in machine learning was used to optimize the factor weights. More reasonable weight values were obtained, which ﬁnally improved the performance of the landslide susceptibility model. Using GPR, the trend of factor values changing with weights can be intuitively displayed, which helps to better grasp the relationship between factors and landslides. This process is primarily derived from interpolation, which indicates that adjacent regions should have the same characteristics. Improving the accuracy of LSM by combining different models and forming a hy- brid model is a common method. At present, many scholars have combined traditional statistical models and opinion-driven models with machine learning-based algorithms, and the performance of the resulting hybrid models is better than that of the original models [9,25,26,74]. These studies show that hybrid models have good application poten- tial, but the key is how to combine models effectively. Machine learning-based models can Appl. Sci. 2022, 12, 10196 24 of 28 mine useful information from a large volume of data, while statistical models have clear mathematical meanings and are conducive to the analysis of the relationships between factors and landslides. Hybrids of both models have been used. The RF-CF (random forest-certainty factor) model proposed by Chen et al. [25], the FT-IV-RF (fractal theory- information value-random forest model) model proposed by Zhao et al. [86], and the EBF-KLR (evidential belief function- kernel logistic regression) model proposed by Chen et al. [74] are innovative combinations of statistical models and machine learning-based models that have been proven to outperform the single models. In this study, a machine learning-based model was used to obtain the distribution pattern of factor weights based on statistical models. The hybrid model combines the advantages of both models, is straight- forward to interpret, and can mine the potential information of factor weights. Therefore, by integrating models, the advantages of different models can be effectively combined, which provides a promising method for landslide susceptibility assessment. 5.3. Limitations of This Study and Prospects of Future Research Although the proposed methods in this study improved the accuracy of landslide susceptibility assessment to a certain extent, certain limitations remain. First, grid units are most commonly used as evaluation units. However, they do not correlate well with real-world geological environments [87]. Therefore, slope units [12] and terrain units [88] have been used in landslide susceptibility assessment. The existing methods for extracting slope units are complicated, and their effect is not ideal. Thus, these methods are not widely used [29]. In addition, the size of grid units also affects the accuracy of landslide susceptibility assessment [89]. Across different study areas, environmental conditions are quite different, and there is no clear criterion for choosing an optimal grid size [56]. In this study, based on literature and expert knowledge as well as considering the computational cost and the actual conditions of the study area, a grid of 30 m 30 m was selected as the evaluation unit. The selection of the optimal evaluation unit is also a difﬁcult problem that should be addressed in future research. Furthermore, in the process of regressing SI weights using GPR, the SI weight value of a class was assigned to the central value of this class. Although this allocation method has brought good results in this study, it still contains some subjectivity. Therefore, future research should consider more reasonable allocation methods to further improve the accuracy of landslide susceptibility assessments. Moreover, considering the second law of geography, a more reasonable screening of regional risk factors should take into account their spatial local heterogeneous (SLH) associations with landslides, and such SLH-based factor screening methods [90,91] are also worthy of continued research in the future. 6. Conclusions For bivariate statistical models such as SI, the distribution of weights does not conform to the reality of factors, which require improvement. Moreover, the selection of factors has a non-negligible impact on the performance of LSM models. This study proposes a hybrid optimization method for the SI model, with the aim of addressing these problems and improving the accuracy and reliability of LSM. The hybrid approach of GeoDetector and RFE was used for factor screening (the obtained model was named GD-SI). The number of factors decreased from 22 to 12, but the AUC value on the testing dataset increased from 0.931 to 0.936. Results show that the prediction performance of the model was improved, proving the effectiveness and reliability of factor screening. Furthermore, the weights of the GD-SI model were optimized using GPR (the obtained model was named GD-GPR-SI). The GD-GPR-SI (AUC = 0.943) model has a higher AUC value than the GD-SI model (AUC = 0.936) on the testing dataset. Therefore, by optimizing GPR, more reasonable weights were obtained, and the predictive ability of the model was improved. The methods proposed in this study improved the predictive ability of the LSM model, which can be used as a general framework for it. The obtained landslide susceptibility maps Appl. Sci. 2022, 12, 10196 25 of 28 can also provide a decision-making basis for landslide prevention and control. Further consideration should be given to the optimization of evaluation units and improvement of the quality of data for modeling. Author Contributions: Conceptualization, Y.Y.; Data curation, Y.Z.; Formal analysis, F.Z.; Investiga- tion, C.S.; Methodology, C.C.; Software, C.C.; Supervision, C.S.; Validation, F.Z.; Visualization, C.S.; Writing—original draft, C.C.; Writing—review & editing, Y.Y. and C.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant num- ber 42071379, 41701448; Technical development project (Potential pipeline threat event identiﬁcation from the perspective of unmanned aerial vehicle) of East Crude Oil Storage and Transportation of National pipe network group Co., Ltd., grant number GWHT20220021074. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data used in this study are available on request from the corre- sponding author. 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Applied Sciences – Multidisciplinary Digital Publishing Institute

Published: Oct 11, 2022

Keywords: landslide susceptibility; statistical index; Gaussian process regression; GeoDetector; recursive feature elimination

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An Optimization of Statistical Index Method Based on Gaussian Process Regression and GeoDetector, for Higher Accurate Landslide Susceptibility Modeling

An Optimization of Statistical Index Method Based on Gaussian Process Regression and GeoDetector, for Higher Accurate Landslide Susceptibility Modeling

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An Optimization of Statistical Index Method Based on Gaussian Process Regression and GeoDetector, for Higher Accurate Landslide Susceptibility Modeling

An Optimization of Statistical Index Method Based on Gaussian Process Regression and GeoDetector, for Higher Accurate Landslide Susceptibility Modeling

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