A Bus Passenger Flow Prediction Model Fused with Point-of-Interest Data Based on Extreme Gradient Boosting

Wanjun Lv; Yongbo Lv; Qi Ouyang; Yuan Ren

doi:10.3390/app12030940

A Bus Passenger Flow Prediction Model Fused with Point-of-Interest Data Based on Extreme Gradient Boosting

Lv, Wanjun;Lv, Yongbo;Ouyang, Qi;Ren, Yuan 2022-01-18 00:00:00 applied sciences Article A Bus Passenger Flow Prediction Model Fused with Point-of-Interest Data Based on Extreme Gradient Boosting 1 1 , 2 1 Wanjun Lv , Yongbo Lv *, Qi Ouyang and Yuan Ren School of Trafﬁc and Transportation, Beijing Jiaotong University, Beijing 100044, China; 18114022@bjtu.edu.cn (W.L.); 7309@bjtu.edu.cn (Y.R.) China Transport Telecommunications & Information Center, Beijing 100011, China; 14114203@bjtu.edu.cn * Correspondence: yblv@bjtu.edu.cn; Tel.: +86-137-0131-3577 Abstract: Bus operation scheduling is closely related to passenger ﬂow. Accurate bus passenger ﬂow prediction can help improve urban bus planning and service quality and reduce the cost of bus operation. Using machine learning algorithms to ﬁnd the rules of urban bus passenger ﬂow has become one of the research hotspots in the ﬁeld of public transportation, especially with the rise of big data technology. Bus IC card data are an important data resource and are more valuable to passenger ﬂow prediction in comparison with manual survey data. Aiming at the balance between efﬁciency and accuracy of passenger ﬂow prediction for multiple lines, we propose a novel passenger ﬂow prediction model based on the point-of-interest (POI) data and extreme gradient boosting (XGBoost), called PFP-XPOI. Firstly, we collected POI data around bus stops based on the Amap Web service application interface. Secondly, three dimensions were considered for building the model. Finally, the XGBoost algorithm was chosen to train the model for each bus line. Results show that the model has higher prediction accuracy through comparison with other models, and thus this method can be used for short-term passenger ﬂow forecasting using bus IC cards. It plays a very important role in providing decision basis for more reﬁned bus operation management. Citation: Lv, W.; Lv, Y.; Ouyang, Q.; Keywords: public transportation; passenger ﬂow prediction; point-of-interest data; extreme gradient Ren, Y. A Bus Passenger Flow boosting algorithm Prediction Model Fused with Point-of-Interest Data Based on Extreme Gradient Boosting. Appl. Sci. 2022, 12, 940. https://doi.org/ 1. Introduction 10.3390/app12030940 Bus transport is a critical component of the transportation system. With the signiﬁcant Academic Editor: Paola Pellegrini progress of urbanization, buses are becoming the leading force in public transportation. Received: 22 November 2021 For example, Beijing has one of the most crowded bus networks at present. According to Accepted: 13 January 2022 the statistics of Beijing Public Transport Corporation, in 2020, there were 1207 bus lines Published: 18 January 2022 (including suburban lines) with a total length of 28,400 km. The volume of the average daily passenger in Beijing has far exceeded a person-time of 5 million, and the total annual Publisher’s Note: MDPI stays neutral passenger volume has reached a person-time of 1.9 billion [1]. Passengers’ behavior can be with regard to jurisdictional claims in understood by analyzing smart card data [2]. The large quantity of data collected by smart published maps and institutional afﬁl- cards offers more detailed characteristics in the time and space dimension than any other iations. types of data. To improve the bus service quality, an accurate and proactive passenger ﬂow prediction approach is necessary [3,4]. Availability of smart card data has offered more opportunities for the prediction work [5]. The prediction results can help the bus operators Copyright: © 2022 by the authors. optimize resource scheduling and save operating costs as well as assist passengers in Licensee MDPI, Basel, Switzerland. making better decisions by adjusting their travel paths and departure time. Furthermore, This article is an open access article this approach is useful for the government to assess risk and guarantee public safety. distributed under the terms and There are two main ﬁelds of study in passenger ﬂow prediction, namely time series conditions of the Creative Commons models and machine learning methods. Most time series models are designed based on Attribution (CC BY) license (https:// the autoregressive integrated moving average model (ARIMA) [6–8]. However, time series creativecommons.org/licenses/by/ models only predict different states for a single target, such as the number of passengers at 4.0/). Appl. Sci. 2022, 12, 940. https://doi.org/10.3390/app12030940 https://www.mdpi.com/journal/applsci Appl. Sci. 2022, 12, 940 2 of 14 a speciﬁc bus stop at different times. When predicting multiple targets for the whole trafﬁc network, this kind of method maintains various models for different objects. As for the machine learning methods, they convert the time series into a supervised learning problem, solved by machine learning algorithms [9]. Passengers’ chief travel destinations are closely related to daily work and life, such as work areas, residential quarters, markets and tourist attractions. The smart card data can be applied to analyze the passenger ﬂow characteristics between different POI locations. From the above point of view, a PFP-XPOI model was investigated in this study for the prediction of bus passenger ﬂow. The main contributions of this study are as follows: A novel bus passenger ﬂow prediction model is proposed. The model takes the predicting accuracy and the predicting efﬁciency into account. The model improves the dimensionality of bus IC card data by fusing POI, so that large-scale low-dimensional data have more feature representation, which ensures the accuracy of prediction. The XGBoost algorithm has the advantage of fast operation, contributing to reducing the total training time of the passenger ﬂow prediction model for multiple lines to achieve the goal of efﬁcient training. Extensive experiments were conducted on historical passenger ﬂow datasets of Beijing. After preprocessing the original data and matching the POI data, the XGBoost algo- rithm can be used to build a uniﬁed prediction model for different stations of the bus line, which can effectively improve the training efﬁciency of the model. In addition, comparison with the existing methods veriﬁes the practicability and effectiveness of the proposed model. In the following, Section 2 reviews literature on bus passenger ﬂow prediction methods. Section 3 elaborates the proposed method in detail, covering data processing and modeling. The prediction results and relevant discussion are given in Section 4. Finally, Section 5 concludes this paper. 2. Related Work Bus passenger ﬂow prediction has been a popular research topic in recent years. Gener- ally, approaches to this topic can be divided into parametric and non-parametric methods. In parametric methods, the ARIMA model has been applied successfully [10]. A pioneering paper [11] introduced ARIMA into trafﬁc prediction. Later, many variants of ARIMA were proposed by combining modes in passenger ﬂow, especially in terms of time. Different seasonal autoregressive integrated moving average (SARIMA) models were tested, and the appropriate one was chosen to generate rail passenger trafﬁc forecasts in [6]. The SARIMA time series model was chosen to forecast the airport terminal passenger ﬂow in [7]. Other methods were further combined with ARIMA by some researchers. A hybrid model combining symbolic regression and ARIMA was proposed to enhance the forecasting accuracy [12]. Fused with a Kalman ﬁlter, the framework consisting of three sequential stages was designed to predict the passenger ﬂow at bus stops [13]. These methods assumed that the data change only over time, so they relied heavily on the similarity of time-varying patterns between historical data and future forecast data, ignoring the role of external inﬂuences. It would be complex for these approaches to train a speciﬁc passenger ﬂow forecasting model for every station in a certain line. Non-parametric models, represented by machine learning methods, were also utilized for predicting trafﬁc characteristics. Machine learning methods have been gaining popu- larity due to their outstanding performance in mining the underlying patterns in trafﬁc dynamics. The support vector machine (SVM)-based approach can map low-dimensional data to a high-dimensional space with kernel functions. The complexity of the computation depends on the number of support vectors rather than the dimensionality of the sample space, which avoids the “dimensionality disaster”. Hybrid models connecting the classical ARIMA and SVM were built in [14], which performed better than the use of a single model. A model combining the advantages of Wavelet and SVM was presented to predict different kinds of passenger ﬂows in the subway system in [15]. These SVM-based methods had Appl. Sci. 2022, 12, 940 3 of 14 satisfying passenger ﬂow forecasting performance. A well-known machine learning pa- per [16] showed that machine learning methods dominate in terms of both accuracy and forecasting horizons. Methods based on deep learning were also applied to passenger flow prediction. Liu et al. proposed a deep learning-based architecture integrating the domain knowledge in transporta- tion modeling to explore short-term metro passenger flow prediction. [17]. The real-time information was taken into consideration in passenger flow prediction based on the LSTM [18]. An improved spatiotemporal long short-term memory model (Sp-LSTM) based on deep learn- ing techniques and big data was developed to forecast short-term outbound passenger volume at urban rail stations in [19]. The XGBoost algorithm is one of the core algorithms in data science and machine learning. XGBoost is an improved CART algorithm. The results of the XGBoost algorithm in a Kaggle machine learning competition were introduced in [20]. Nielsen explained why XGBoost wins every machine learning competition in his master ’s thesis [21]. Dong et al. predicted short-term trafﬁc ﬂow using XGBoost and compared its accuracy with that of SVM [22]. Lee et al. trained XGBoost to model express train preference using smart card and train log data and achieved notable accuracy [23]. Mass data are an important condition for the algorithm to function. The availability of big data sources such as smart card data and POI provide a perfect chance to produce new insights into transport demand modeling [24]. Smart card records, the transactions of passengers in the public transit network, are a valuable source of urban mobility data [25]. In order to ensure the prediction accuracy, it is vital to increase the dimensions of bus smart card data. By introducing POI data to characterize the attributes of certain areas, the model could be more fully trained to improve accuracy [26]. Accordingly, combining the POI and smart card data has the potential to reveal trip purposes of passengers. To balance the efﬁciency and accuracy of prediction, we propose a novel passenger ﬂow prediction model based on extreme gradient boosting (XGBoost) and the point-of- interest (POI) data, referred to as PFP-XPOI. 3. Methodology 3.1. IC Card Data Processing and POI Description The target data for this study were the number of passengers boarding and alighting at each bus station of the two selected routes during the morning peak hours (7:00–9:00, with a half-hour interval containing four time periods). The two selected bus routes are line 56008 and line 685. The bus route 56008 is a bus loop that passes through the central business district (CBD) and has a very large passenger ﬂow, while the bus route 685 has a relatively small passenger ﬂow, and the two routes interchange at Fangzhuangqiaoxi bus station. The PFP-XPOI model training set is from 8 October 2015 to 25 October 2015, and the test set is from 26 October 2015 to 30 October 2015. The total size of the dataset is 50 GB, containing 150 million swipe records. After being clustered by station and time period, the total number of data is 3 million. The process of cleaning the IC card data is to remove the data with empty boarding or alighting time, and to delete the data with an interval of more than 3 h from boarding to alighting time. The cleaned data account for about 1% of the total data. POI is a term in GIS which refers to all geographical objects that can be abstracted as points, especially some geographical entities that are closely related to people’s life, such as schools, banks, restaurants, gas stations, hospitals and supermarkets. The main use of POI is to describe the address of things or events, and the number of different types of POI in a region can characterize the attributes of the region. In this study, POI data collection around bus stops was carried out based on the Amap application programming interface (API). The API refers to a series of functions that have been predeﬁned. Developers can implement existing functions by calling API functions without accessing the source code or understanding the details of internal working mechanisms. The Amap location based services (LBS) open platform provides professional electronic maps and location services to the public. When developers integrate the corresponding software development kit (SDK), Appl. Sci. 2022, 12, 940 4 of 14 the interface can be invoked to implement many functions, such as map display, label POI, location retrieval, data storage and analysis. The collection process is divided into four parts: acquiring global positioning system (GPS) latitude and longitude of each station based on bus operation data, converting GPS latitude and longitude into Amap coordinates, collecting POI information based on Amap coordinates and organizing POI data into corresponding ﬁelds. To convert GPS coordinates to Amap coordinates, we need to apply the coordinate conversion method and add the corresponding parameters to the URL of the GET request. The main parameters for applying this method are listed in Table 1. Table 1. Coordinate conversion and peripheral searching parameters using Amap API. Parameter Meaning key Users apply for API types on the ofﬁcial website of AMap. Longitude and latitude are divided by “,”. Longitude is the location former and latitude is the latter. The decimal point of latitude and longitude should not exceed 6 digits. coordsys The original coordinate system. POI types. The classiﬁcation code consists of six digits. The ﬁrst types two numbers represent large categories, the middle two represent medium categories and the last two represent small categories. city City of inquiry. radius Radius of the inquiry. The value range is from 0 to 50,000. Output Return to data format type. 3.2. Passenger Flow Prediction Model We propose the PFP-XPOI model for passenger ﬂow prediction. The features selected for this model comprise the following three dimensions. One dimension is the information related to the line and the station, such as the line code of the station and the latitude and longitude of the station. Another dimension is the time period and the date when the IC card data are generated. The third dimension is the number of different types of POI around the station, including the number of companies and research institutions, etc. This model consists of two parts. One part is the calibration of the service radius between the bus station and POI data, and the other part is the training of the passenger ﬂow prediction model for each line. We built the PFP-XPOI model based on the following steps. The dataset D is a sample space, and we can represent the machine learning model as M(x 2 D ) ! y. (1) where M means a mapping from data point x to its true value y. After taking POI into account, we can add a new dataset to the original one. Namely D = f (D , D ). (2) n dis S P where D is the updated sample space. D means the POI data set. f refers to a distance- n P dis based function between bus stations and POI. In this model, distances were set to 100, 200, 300, 400 and 500 m, forming 5 datasets. After that, to obtain the optimal service radius d*, the machine learning model for different datasets was trained. Finally, d* can help us ﬁnd the best dataset. We trained a passenger ﬂow prediction model for each line based on this dataset using XGBoost. The detail of the PFP-XPOI model is shown in Figure 1. Appl. Sci. 2022, 12, x FOR PEER REVIEW 5 of 14 100, 200, 300, 400 and 500 m, forming 5 datasets. After that, to obtain the optimal service radius d*, the machine learning model for different datasets was trained. Finally, d* can Appl. Sci. 2022, 12, 940 help us find the best dataset. We trained a passenger flow prediction model for each line 5 of 14 based on this dataset using XGBoost. The detail of the PFP-XPOI model is shown in Figure Figure 1. The process and organization of the PFP-XPOI model. Figure 1. The process and organization of the PFP-XPOI model. 3.3. Model Training 3.3. Model Training In this research, XGBoost was used to train the model for every bus line. XGBoost is In this research, XGBoost was used to train the model for every bus line. XGBoost scalable in a wide range of situations because of the optimization of some important algo- is scalable in a wide range of situations because of the optimization of some important rithms and systems, including a novel tree learning algorithm for handling sparse data algorithms and systems, including a novel tree learning algorithm for handling sparse and a rational weighted quantile sketch process for controlling instance weights in ap- data and a rational weighted quantile sketch process for controlling instance weights in proximate tree learning. Its operating time is 10 times faster than other popular programs approximate tree learning. Its operating time is 10 times faster than other popular programs on a single device, and it scales up to billions of examples in the case of distributed or on a single device, and it scales up to billions of examples in the case of distributed or limited limited memory. Parallel and distributed computing makes learning faster which enables memory. Parallel and distributed computing makes learning faster which enables quicker quicker model exploration. In addition, utilization of out-of-core calculation enables hun- model exploration. In addition, utilization of out-of-core calculation enables hundred dred millions of examples to be processed on a desktop. These techniques can be con- millions of examples to be processed on a desktop. These techniques can be connected to nected to create an end-to-end system that extends to big data with the fewest cluster cr resourc eate an es.end-to-end system that extends to big data with the fewest cluster resources. XGBoost is one kind of boosting tree model aiming to generate certain tree models XGBoost is one kind of boosting tree model aiming to generate certain tree models for prediction. The tree ensemble model includes independent variable 𝑥 and dependent for prediction. The tree ensemble model includes independent variable 𝑖 x and dependent variable y and estimates the target value y using T additive functions. The function can be expressed as y = f(x ) = f (x ) (3) i å t i t=1 where y is the target value; y is the dependent variable (y is 1 if the passenger boards on i i or alights from the bus; otherwise, it is 0); x is the independent variable; t is the features; f (x ) is the model at the tth iteration and T is the number of tree functions. t i (t) The objective is to minimize the loss function L at the tth iteration which can be expressed as n (t1) (t) L = l y , y + f (x ) + W( f ) (4) t t å i i i=1 Appl. Sci. 2022, 12, 940 6 of 14 (t1) where l represents the loss function and y means the predicted value of the (t 1)th iteration. The additional term W( f ) plays a role in reducing the complexity of the model. (t1) (t) Approximating L with a second-order Taylor expansion for l y , y + f (x ) at i i (t1) y , the Equation (4) becomes (t1) (t) 2 L ' [l y , y ) + g f (x ) + h f (x )] + W( f ) (5) å i i t i i i t i=1 i (t1) (t1) ¶l y ,y ¶ l y ,y i i i i where g = , h = . i i (t1) (t1) ¶y ¶y i i (t1) l y , y in Equation (5) can be disregarded as it is a constant term. Therefore, we obtain a new simpliﬁed objective function as follows. n 1 (t) 2 L = [g f (x ) + h f (x )] + W( f ) (6) å i t i i i t i=1 For a tree structure, the samples can be grouped according to the leaf node, and the samples that fall into the same leaf node can be represented as I = i x 2 j . j is the f j g j i leaf node number. By introducing w as the score of leaf j, we can rewrite Equation (6) as follows. n 1 1 T (t) 2 2 L = [g f (x ) + h f (x )] + gT + l w å å i t i i i i=1 t j=1 2 2 j T (7) T 1 2 = l [ g w + h + l w ] + gT å å å å i2I i j i2I i j=1 2 j j j j=1 where g controls the number of leaf nodes and l prevents overﬁtting. Let the value of the ﬁrst-order partial derivative function of y concerning x be equal to 0, and then the optimal weight w of leaf j can be calculated as w = (8) H + l (t) L can ﬁnally be shown in Equation (9). 1 T G (t) L = + gT (9) j=1 2 H + l Normally it is impossible to enumerate all the possible tree structures. A greedy algorithm that starts from a single leaf and iteratively adds branches to the tree is used instead. Assume that I and I are the instance sets of left and right nodes after the split. L R Let I = I [ I , and then the loss reduction after the split is given by L R 1 G G G L R L = + g. (10) spilt 2 H + l H + l H + l L R With the help of the process above, we can calculate a tree for prediction. 4. Results and Discussion 4.1. Peak Period Experiments The training dataset used was extracted from 8 October 2015 to 25 October 2015. The test dataset is from 26 October 2015 to 30 October 2015. The two lines are 685 and 56008. Line 56008 has a large passenger volume because it is a major bus line on the third ring road in Beijing. Line 685 is a normal line that has a relatively small passenger volume. If the passenger numbers of the two lines are very large, the departure frequency will be relatively high; thus, we do not need to consider the transfer situation. If the passenger numbers of both lines are small, the number of passengers who need to transfer between Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 14 4. Results and Discussion 4.1. Peak Period Experiments The training dataset used was extracted from 8 October 2015 to 25 October 2015. The test dataset is from 26 October 2015 to 30 October 2015. The two lines are 685 and 56008. Line 56008 has a large passenger volume because it is a major bus line on the third ring road in Beijing. Line 685 is a normal line that has a relatively small passenger volume. If the passenger numbers of the two lines are very large, the departure frequency will be relatively high; thus, we do not need to consider the transfer situation. If the passenger Appl. Sci. 2022, 12, 940 7 of 14 numbers of both lines are small, the number of passengers who need to transfer between lines will be much smaller, so there is little need to consider the transfer coordination. Therefore, after calculation, we chose these two lines as our experimental lines. These two lines will be much smaller, so there is little need to consider the transfer coordination. lines can be transferred at Fangzhuangqiaoxi bus station. Therefore, after calculation, we chose these two lines as our experimental lines. These two With a Windows 10 operating system, a I7-8700k processor, and 32 GB memory, the lines can be transferred at Fangzhuangqiaoxi bus station. PFP-XPOI model takes 20 min to finish the process of determining the station query radius With a Windows 10 operating system, a I7-8700k processor, and 32 GB memory, the totally, and the process is executed only once after the general rule is obtained. In the PFP-XPOI model takes 20 min to ﬁnish the process of determining the station query radius process of passenger flow prediction, the total time for training a single-route passenger totally, and the process is executed only once after the general rule is obtained. In the flow prediction model is 4 min, while training a single-route CART model and a model process of passenger ﬂow prediction, the total time for training a single-route passenger such as SVM takes about 8 min, and the recurrent neural network (RNN) method with ﬂow prediction model is 4 min, while training a single-route CART model and a model seven steps takes about 6 h. such as SVM takes about 8 min, and the recurrent neural network (RNN) method with The root mean square error (RMSE) was selected to evaluate the model. The RMSE seven steps takes about 6 h. can be calculated by Equation (11). The root mean square error (RMSE) was selected to evaluate the model. The RMSE can be calculated by Equation (11). √ (11) | | RMSE = ∑ 𝑦 − 𝑦 ̂ 𝑚 𝑚 𝑚 =1 RMSE = y y ˆ (11) j j å m m m=1 where 𝑀 is the total number of samples. 𝑦 is the true value, and 𝑦 ̂ is the predicted 𝑚 𝑚 value. where M is the total number of samples. y is the true value, and y ˆ is the predicted value. m m For line 56008, the optimal parameters of the predicted model are as follows. The For line 56008, the optimal parameters of the predicted model are as follows. The maximum tree depth is four layers. The learning rate is 0.02. The maximum tree size is maximum tree depth is four layers. The learning rate is 0.02. The maximum tree size is 1500, and the optimal distance is 300 m. For line 685, the optimal parameters of the model 1500, and the optimal distance is 300 m. For line 685, the optimal parameters of the model are as follows. The maximum tree depth is three layers. The learning rate is 0.01. The max- are as follows. The maximum tree depth is three layers. The learning rate is 0.01. The imum size of the tree is 800, and the optimal distance is 300 m. The evaluation of the pre- maximum size of the tree is 800, and the optimal distance is 300 m. The evaluation of the diction model for lines 56008 and 685 under different distances is shown in Figure 2. prediction model for lines 56008 and 685 under different distances is shown in Figure 2. Figure Figure 2. 2. The The R RMSE MSE and and distance distance of of passenger passenger num number ber pr pre ediction diction model in model in lines lines56008 56008 and and 685. 685. For line 56008, the ﬁgure reﬂects that the RMSE value of the test set reaches the For line 56008, the figure reflects that the RMSE value of the test set reaches the min- minimum at a distance of 300 m, namely where the error of the prediction model is the imum at a distance of 300 m, namely where the error of the prediction model is the small- smallest, about 7.7. When the distance is 500 and 100 m, the RMSE is lager. Similarly, est, about 7.7. When the distance is 500 and 100 m, the RMSE is lager. Similarly, for line for line 685, the minimum of RSME value is also found at a distance of 300 m, about 4.9. 685, the minimum of RSME value is also found at a distance of 300 m, about 4.9. However, However, the effect of different distances on the accuracy of the model in line 685 is smaller than that in line 56008. The results suggest that grouping the data by lines and training one model for each line can reduce the interference between different lines and effectively reduce the prediction error. We divided the early peak period into four sections with an interval of 30 min. Taking samples on 28 October 2015 as an example, the predicted values and true values of on-board and alighting passenger numbers of line 56008 are shown in Figures 3 and 4, respectively. Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 of 14 Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 of 14 the effect of different distances on the accuracy of the model in line 685 is smaller than the effect of different distances on the accuracy of the model in line 685 is smaller than that in line 56008. The results suggest that grouping the data by lines and training one that in line 56008. The results suggest that grouping the data by lines and training one model for each line can reduce the interference between different lines and effectively re- model for each line can reduce the interference between different lines and effectively re- duce the prediction error. duce the prediction error. We divided the early peak period into four sections with an interval of 30 min. Taking We divided the early peak period into four sections with an interval of 30 min. Taking samples on 28 October 2015 as an example, the predicted values and true values of on- Appl. Sci. 2022, 12, 940 8 of 14 samples on 28 October 2015 as an example, the predicted values and true values of on- board and alighting passenger numbers of line 56008 are shown in Figures 3 and 4, re- board and alighting passenger numbers of line 56008 are shown in Figures 3 and 4, re- spectively. spectively. Figure 3. Prediction and true values of on-board passenger number for line 56008. Figure 3. Prediction and true values of on-board passenger number for line 56008. Figure 3. Prediction and true values of on-board passenger number for line 56008. Figure 4. Prediction and true values of alighting passenger number for line 56008. The number of passengers boarding from 7:00 to 8:00 on line 56008 was signiﬁcantly greater than that from 8:00 to 9:00. There were two main boarding stations for line 56008, namely stations 6 and 16. The peak boarding passenger ﬂow on line 56008 was about 230. Compared with on-board passengers, the distribution of alighting passengers between 7:00 to 8:00 and 8:00 to 9:00 was more balanced, and the total number of alighting passengers was not obviously different between the two periods. However, from 7:00 to 8:00, the stations where passengers alighted were more concentrated. Stations 8 and 22 were the two main drop-off stations of line 56008. The peak alighting ﬂow of line 56008 was about 240. Appl. Sci. 2022, 12, x FOR PEER REVIEW 9 of 14 Figure 4. Prediction and true values of alighting passenger number for line 56008. The number of passengers boarding from 7:00 to 8:00 on line 56008 was significantly greater than that from 8:00 to 9:00. There were two main boarding stations for line 56008, namely stations 6 and 16. The peak boarding passenger flow on line 56008 was about 230. Compared with on-board passengers, the distribution of alighting passengers between 7:00 to 8:00 and 8:00 to 9:00 was more balanced, and the total number of alighting passen- Appl. Sci. 2022, 12, 940 9 of 14 gers was not obviously different between the two periods. However, from 7:00 to 8:00, the stations where passengers alighted were more concentrated. Stations 8 and 22 were the two main drop-off stations of line 56008. The peak alighting flow of line 56008 was about In comparison with line 56008, the passenger ﬂow of line 685 had decreased signif- In comparison with line 56008, the passenger flow of line 685 had decreased signifi- icantly. The on-board passenger ﬂow from 8:00 to 9:00 was greater than that from 7:00 cantly. The on-board passenger flow from 8:00 to 9:00 was greater than that from 7:00 to to 8:00. During the two periods, stations 1 to 5 were the main pick-up stations, and the 8:00. During the two periods, stations 1 to 5 were the main pick-up stations, and the peak peak passenger ﬂow for boarding was about 50. Stations 6 and 9 were the main drop-off passenger flow for boarding was about 50. Stations 6 and 9 were the main drop-off sta- stations. Station 6 was the transfer station of Lines 685 and 56008, so a group of passengers tions. Station 6 was the transfer station of Lines 685 and 56008, so a group of passengers chose to get off at this station. The peak alighting ﬂow was about 60. The details of the chose to get off at this station. The peak alighting flow was about 60. The details of the predicted values and the real values for on-board and alighting passengers are shown in predicted values and the real values for on-board and alighting passengers are shown in Figur Figure es s 55 an and d 6, respect 6, respectively ively. . Appl. Sci. 2022, 12, x FOR PEER REVIEW 10 of 14 Figure 5. Prediction and true values of on-board passenger numbers for line 685. Figure 5. Prediction and true values of on-board passenger numbers for line 685. Figure Figure 6. 6. Predi Prediction ction and and tru tr e values ue values of al of ighting alighting passeng passenger er number numbers s for line 685 for line . 685. 4.2. Impact Analysis of POI There were 23 specific features selected in the PFP-XPOI model for passenger flow forecasting, and the feature importance is shown in Figure 7. Figure 7. The feature importance of different XGBoost models with POI data (a) and without POI data (b). The times of node split were used as the feature importance in the XGBoost algo- rithm. The more times a feature splits, the more important it is. Figure 7 shows the feature Appl. Sci. 2022, 12, x FOR PEER REVIEW 10 of 14 Figure 6. Prediction and true values of alighting passenger numbers for line 685. Appl. Sci. 2022, 12, 940 10 of 14 4.2. Impact Analysis of POI There were 23 specific features selected in the PFP-XPOI model for passenger flow 4.2. Impact Analysis of POI forecasting, and the feature importance is shown in Figure 7. There were 23 speciﬁc features selected in the PFP-XPOI model for passenger ﬂow forecasting, and the feature importance is shown in Figure 7. Figure 7. The feature importance of different XGBoost models with POI data (a) and without POI data (b). Figure 7. The feature importance of different XGBoost models with POI data (a) and without POI data (b). The times of node split were used as the feature importance in the XGBoost algorithm. The more times a feature splits, the more important it is. Figure 7 shows the feature impor- The times of node split were used as the feature importance in the XGBoost algo- tance of different models. PFP-XPOI uses the XGBoost algorithm to train the passenger ﬂow rithm. The more times a feature splits, the more important it is. Figure 7 shows the feature prediction model. After the POI data are fused, the feature importance of the model will change signiﬁcantly. When POI data are not used, the model mainly splits by the station index, which makes this feature signiﬁcant in the split process. In the case of modeling with POI data, the model splits more evenly at different features. The effect of the POI data on the passenger ﬂow prediction for line 56008 is described directly in Figures 8 and 9. They illustrate the predicted values of on-board and alighting passenger number from 7:00 to 7:30 on 29 October 2015. The predicted values of XGBoost and the historical average model are almost the same. According to this phenomenon, we can draw conclusions in accordance with the results shown in Figure 7. The major split point of the XGBoost model is the index of stations. After the calibration of the service radius between bus stations and POI data, the PFP-XPOI model has a better performance than other models in passenger ﬂow prediction. 4.3. Comparison with Multiple Models To verify the accuracy of the PFP-XPOI model, this study compared the performance of different models as listed in Tables 2–5. We used the RMSE, mean absolute error (MAE) and R-squared to evaluate different models. The MAE can be expressed as 1 M MAE = jy y ˆ j (12) å m m m=1 where M is the total number of samples. y is the true value, and y ˆ is the predicted value. m m R-squared can be expressed as å (y y ˆ ) m m m=1 R squared = 1 (13) M 2 y y å ( ) m=1 m Appl. Sci. 2022, 12, x FOR PEER REVIEW 11 of 14 importance of different models. PFP-XPOI uses the XGBoost algorithm to train the pas- senger flow prediction model. After the POI data are fused, the feature importance of the model will change significantly. When POI data are not used, the model mainly splits by the station index, which makes this feature significant in the split process. In the case of modeling with POI data, the model splits more evenly at different features. The effect of the POI data on the passenger flow prediction for line 56008 is described directly in Figures 8 and 9. They illustrate the predicted values of on-board and alighting passenger number from 7:00 to 7:30 on 29 October 2015. The predicted values of XGBoost Appl. Sci. 2022, 12, 940 11 of 14 and the historical average model are almost the same. According to this phenomenon, we can draw conclusions in accordance with the results shown in Figure 7. The major split point of the XGBoost model is the index of stations. After the calibration of the service where M is the total number of samples. y is the true value. y ˆ is the predicted value, and radius between bus stations and POI data, the m PFP-XPOI model hasm a better performance y is the mean of samples. than other models in passenger flow prediction. Appl. Sci. 2022, 12, x FOR PEER REVIEW 12 of 14 Figure 8. Predicted and true values of on-board passenger numbers using three models. Figure 8. Predicted and true values of on-board passenger numbers using three models. Figure 9. Predicted and true values of alighting passenger numbers using three models. Figure 9. Predicted and true values of alighting passenger numbers using three models. 4.3. Comparison with Multiple Models To verify the accuracy of the PFP-XPOI model, this study compared the performance of different models as listed in Tables 2–5. We used the RMSE, mean absolute error (MAE) and R-squared to evaluate different models. The MAE can be expressed as MAE = ∑ |𝑦 − 𝑦 ̂ | (12) 𝑚 𝑚 𝑚 =1 where 𝑀 is the total number of samples. 𝑦 is the true value, and 𝑦 ̂ is the predicted 𝑚 𝑚 value. R-squared can be expressed as 𝑀 2 (𝑦 − 𝑦 ̂ ) 𝑚 =1 𝑚 𝑚 R − squared = 1 − (13) 𝑀 2 ∑ (𝑦 − 𝑦 ̅ ) 𝑚 𝑚 𝑚 =1 where 𝑀 is the total number of samples. 𝑦 is the true value. 𝑦 ̂ is the predicted value, 𝑚 𝑚 and 𝑦 ̅ is the mean of samples. Table 2. Evaluation values of different models for on-board passenger prediction in line 56008. On-Board Passenger Prediction Models in Line 56008 RMSE MAE R-Squared PFP-XPOI 7.84 7.32 0.912 XGBoost 8.79 8.16 0.889 LSTM 8.69 8.12 0.892 SVM 8.89 8.25 0.887 Historical Average 8.96 8.34 0.885 Table 3. Evaluation values of different models for alighting passenger prediction in line 56008. Alighting Passenger Prediction Models in Line 56008 RMSE MAE R-Squared PFP-XPOI 7.43 6.98 0.931 XGBoost 8.06 7.52 0.919 LSTM 7.49 7.13 0.929 SVM 7.96 7.48 0.921 Historical Average 8.12 7.65 0.917 Appl. Sci. 2022, 12, 940 12 of 14 Table 2. Evaluation values of different models for on-board passenger prediction in line 56008. On-Board Passenger Prediction Models in RMSE MAE R-Squared Line 56008 PFP-XPOI 7.84 7.32 0.912 XGBoost 8.79 8.16 0.889 LSTM 8.69 8.12 0.892 SVM 8.89 8.25 0.887 Historical Average 8.96 8.34 0.885 Table 3. Evaluation values of different models for alighting passenger prediction in line 56008. Alighting Passenger Prediction Models in RMSE MAE R-Squared Line 56008 PFP-XPOI 7.43 6.98 0.931 XGBoost 8.06 7.52 0.919 LSTM 7.49 7.13 0.929 SVM 7.96 7.48 0.921 Historical Average 8.12 7.65 0.917 Table 4. Evaluation values of different models for on-board passenger prediction in line 685. On-Board Passenger Prediction Models in RMSE MAE R-Squared Line 685 PFP-XPOI 4.92 4.53 0.890 XGBoost 5.76 4.74 0.849 LSTM 5.32 4.66 0.871 SVM 6.09 4.90 0.831 Historical Average 5.53 4.92 0.861 Table 5. Evaluation values of different models for alighting passenger prediction in line 685. Alighting Passenger Prediction Models in RMSE MAE R-Squared Line 685 PFP-XPOI 4.73 4.34 0.925 XGBoost 5.48 5.02 0.899 LSTM 5.13 4.97 0.912 SVM 5.53 5.12 0.898 Historical Average 5.69 5.14 0.892 Results reveal that the PFP-XPOI performs best, followed by LSTM and XGBoost. This phenomenon is similar to that obtained by Spyros Makridakis [16]. Because the alighting passenger ﬂow is more stable, the alighting passenger ﬂow prediction model is more accurate than the on-board passenger ﬂow prediction model for both lines. The results demonstrate that the PFP-XPOI model performs better in prediction and improves the prediction accuracy due to the addition of new features. The historical average data cannot effectively take the impact of week, POI and other factors into account so the error is relatively large. The error of using XGBoost model individually is similar to that of the historical mean. This also indicates that the direct application of XGBoost model for passenger ﬂow prediction is mainly based on the station index. 5. Conclusions Based on IC card data of Beijing buses, this study addressed the bus passenger ﬂow prediction problem via fusing POI data by using the XGBoost algorithm. The proposed Appl. Sci. 2022, 12, 940 13 of 14 method takes advantage of the accuracy ensured by POI generated from bus operation data and the efﬁciency guaranteed by the XGBoost algorithm. Through the XGBoost algorithm, the big data of the bus card can be merged with the POI data. After calculating the experimental data, we chose “300 m” as the query radius because the prediction outcome is the most accurate. Due to some new added features, the PFP-XPOI model can improve the dimension of smart card data by fusing the POI data. By comparison and veriﬁcation, it was proved that the proposed model has higher accuracy and runs faster. This work may be further strengthened in other ﬁelds. The modeling of multiple buses arriving and leaving a single bus station would require more in-depth analysis. In the future, we will explore the applications of the proposed method in intelligent transportation system comprehensively. 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Abstract

applied sciences Article A Bus Passenger Flow Prediction Model Fused with Point-of-Interest Data Based on Extreme Gradient Boosting 1 1 , 2 1 Wanjun Lv , Yongbo Lv *, Qi Ouyang and Yuan Ren School of Trafﬁc and Transportation, Beijing Jiaotong University, Beijing 100044, China; 18114022@bjtu.edu.cn (W.L.); 7309@bjtu.edu.cn (Y.R.) China Transport Telecommunications & Information Center, Beijing 100011, China; 14114203@bjtu.edu.cn * Correspondence: yblv@bjtu.edu.cn; Tel.: +86-137-0131-3577 Abstract: Bus operation scheduling is closely related to passenger ﬂow. Accurate bus passenger ﬂow prediction can help improve urban bus planning and service quality and reduce the cost of bus operation. Using machine learning algorithms to ﬁnd the rules of urban bus passenger ﬂow has become one of the research hotspots in the ﬁeld of public transportation, especially with the rise of big data technology. Bus IC card data are an important data resource and are more valuable to passenger ﬂow prediction in comparison with manual survey data. Aiming at the balance between efﬁciency and accuracy of passenger ﬂow prediction for multiple lines, we propose a novel passenger ﬂow prediction model based on the point-of-interest (POI) data and extreme gradient boosting (XGBoost), called PFP-XPOI. Firstly, we collected POI data around bus stops based on the Amap Web service application interface. Secondly, three dimensions were considered for building the model. Finally, the XGBoost algorithm was chosen to train the model for each bus line. Results show that the model has higher prediction accuracy through comparison with other models, and thus this method can be used for short-term passenger ﬂow forecasting using bus IC cards. It plays a very important role in providing decision basis for more reﬁned bus operation management. Citation: Lv, W.; Lv, Y.; Ouyang, Q.; Keywords: public transportation; passenger ﬂow prediction; point-of-interest data; extreme gradient Ren, Y. A Bus Passenger Flow boosting algorithm Prediction Model Fused with Point-of-Interest Data Based on Extreme Gradient Boosting. Appl. Sci. 2022, 12, 940. https://doi.org/ 1. Introduction 10.3390/app12030940 Bus transport is a critical component of the transportation system. With the signiﬁcant Academic Editor: Paola Pellegrini progress of urbanization, buses are becoming the leading force in public transportation. Received: 22 November 2021 For example, Beijing has one of the most crowded bus networks at present. According to Accepted: 13 January 2022 the statistics of Beijing Public Transport Corporation, in 2020, there were 1207 bus lines Published: 18 January 2022 (including suburban lines) with a total length of 28,400 km. The volume of the average daily passenger in Beijing has far exceeded a person-time of 5 million, and the total annual Publisher’s Note: MDPI stays neutral passenger volume has reached a person-time of 1.9 billion [1]. Passengers’ behavior can be with regard to jurisdictional claims in understood by analyzing smart card data [2]. The large quantity of data collected by smart published maps and institutional afﬁl- cards offers more detailed characteristics in the time and space dimension than any other iations. types of data. To improve the bus service quality, an accurate and proactive passenger ﬂow prediction approach is necessary [3,4]. Availability of smart card data has offered more opportunities for the prediction work [5]. The prediction results can help the bus operators Copyright: © 2022 by the authors. optimize resource scheduling and save operating costs as well as assist passengers in Licensee MDPI, Basel, Switzerland. making better decisions by adjusting their travel paths and departure time. Furthermore, This article is an open access article this approach is useful for the government to assess risk and guarantee public safety. distributed under the terms and There are two main ﬁelds of study in passenger ﬂow prediction, namely time series conditions of the Creative Commons models and machine learning methods. Most time series models are designed based on Attribution (CC BY) license (https:// the autoregressive integrated moving average model (ARIMA) [6–8]. However, time series creativecommons.org/licenses/by/ models only predict different states for a single target, such as the number of passengers at 4.0/). Appl. Sci. 2022, 12, 940. https://doi.org/10.3390/app12030940 https://www.mdpi.com/journal/applsci Appl. Sci. 2022, 12, 940 2 of 14 a speciﬁc bus stop at different times. When predicting multiple targets for the whole trafﬁc network, this kind of method maintains various models for different objects. As for the machine learning methods, they convert the time series into a supervised learning problem, solved by machine learning algorithms [9]. Passengers’ chief travel destinations are closely related to daily work and life, such as work areas, residential quarters, markets and tourist attractions. The smart card data can be applied to analyze the passenger ﬂow characteristics between different POI locations. From the above point of view, a PFP-XPOI model was investigated in this study for the prediction of bus passenger ﬂow. The main contributions of this study are as follows: A novel bus passenger ﬂow prediction model is proposed. The model takes the predicting accuracy and the predicting efﬁciency into account. The model improves the dimensionality of bus IC card data by fusing POI, so that large-scale low-dimensional data have more feature representation, which ensures the accuracy of prediction. The XGBoost algorithm has the advantage of fast operation, contributing to reducing the total training time of the passenger ﬂow prediction model for multiple lines to achieve the goal of efﬁcient training. Extensive experiments were conducted on historical passenger ﬂow datasets of Beijing. After preprocessing the original data and matching the POI data, the XGBoost algo- rithm can be used to build a uniﬁed prediction model for different stations of the bus line, which can effectively improve the training efﬁciency of the model. In addition, comparison with the existing methods veriﬁes the practicability and effectiveness of the proposed model. In the following, Section 2 reviews literature on bus passenger ﬂow prediction methods. Section 3 elaborates the proposed method in detail, covering data processing and modeling. The prediction results and relevant discussion are given in Section 4. Finally, Section 5 concludes this paper. 2. Related Work Bus passenger ﬂow prediction has been a popular research topic in recent years. Gener- ally, approaches to this topic can be divided into parametric and non-parametric methods. In parametric methods, the ARIMA model has been applied successfully [10]. A pioneering paper [11] introduced ARIMA into trafﬁc prediction. Later, many variants of ARIMA were proposed by combining modes in passenger ﬂow, especially in terms of time. Different seasonal autoregressive integrated moving average (SARIMA) models were tested, and the appropriate one was chosen to generate rail passenger trafﬁc forecasts in [6]. The SARIMA time series model was chosen to forecast the airport terminal passenger ﬂow in [7]. Other methods were further combined with ARIMA by some researchers. A hybrid model combining symbolic regression and ARIMA was proposed to enhance the forecasting accuracy [12]. Fused with a Kalman ﬁlter, the framework consisting of three sequential stages was designed to predict the passenger ﬂow at bus stops [13]. These methods assumed that the data change only over time, so they relied heavily on the similarity of time-varying patterns between historical data and future forecast data, ignoring the role of external inﬂuences. It would be complex for these approaches to train a speciﬁc passenger ﬂow forecasting model for every station in a certain line. Non-parametric models, represented by machine learning methods, were also utilized for predicting trafﬁc characteristics. Machine learning methods have been gaining popu- larity due to their outstanding performance in mining the underlying patterns in trafﬁc dynamics. The support vector machine (SVM)-based approach can map low-dimensional data to a high-dimensional space with kernel functions. The complexity of the computation depends on the number of support vectors rather than the dimensionality of the sample space, which avoids the “dimensionality disaster”. Hybrid models connecting the classical ARIMA and SVM were built in [14], which performed better than the use of a single model. A model combining the advantages of Wavelet and SVM was presented to predict different kinds of passenger ﬂows in the subway system in [15]. These SVM-based methods had Appl. Sci. 2022, 12, 940 3 of 14 satisfying passenger ﬂow forecasting performance. A well-known machine learning pa- per [16] showed that machine learning methods dominate in terms of both accuracy and forecasting horizons. Methods based on deep learning were also applied to passenger flow prediction. Liu et al. proposed a deep learning-based architecture integrating the domain knowledge in transporta- tion modeling to explore short-term metro passenger flow prediction. [17]. The real-time information was taken into consideration in passenger flow prediction based on the LSTM [18]. An improved spatiotemporal long short-term memory model (Sp-LSTM) based on deep learn- ing techniques and big data was developed to forecast short-term outbound passenger volume at urban rail stations in [19]. The XGBoost algorithm is one of the core algorithms in data science and machine learning. XGBoost is an improved CART algorithm. The results of the XGBoost algorithm in a Kaggle machine learning competition were introduced in [20]. Nielsen explained why XGBoost wins every machine learning competition in his master ’s thesis [21]. Dong et al. predicted short-term trafﬁc ﬂow using XGBoost and compared its accuracy with that of SVM [22]. Lee et al. trained XGBoost to model express train preference using smart card and train log data and achieved notable accuracy [23]. Mass data are an important condition for the algorithm to function. The availability of big data sources such as smart card data and POI provide a perfect chance to produce new insights into transport demand modeling [24]. Smart card records, the transactions of passengers in the public transit network, are a valuable source of urban mobility data [25]. In order to ensure the prediction accuracy, it is vital to increase the dimensions of bus smart card data. By introducing POI data to characterize the attributes of certain areas, the model could be more fully trained to improve accuracy [26]. Accordingly, combining the POI and smart card data has the potential to reveal trip purposes of passengers. To balance the efﬁciency and accuracy of prediction, we propose a novel passenger ﬂow prediction model based on extreme gradient boosting (XGBoost) and the point-of- interest (POI) data, referred to as PFP-XPOI. 3. Methodology 3.1. IC Card Data Processing and POI Description The target data for this study were the number of passengers boarding and alighting at each bus station of the two selected routes during the morning peak hours (7:00–9:00, with a half-hour interval containing four time periods). The two selected bus routes are line 56008 and line 685. The bus route 56008 is a bus loop that passes through the central business district (CBD) and has a very large passenger ﬂow, while the bus route 685 has a relatively small passenger ﬂow, and the two routes interchange at Fangzhuangqiaoxi bus station. The PFP-XPOI model training set is from 8 October 2015 to 25 October 2015, and the test set is from 26 October 2015 to 30 October 2015. The total size of the dataset is 50 GB, containing 150 million swipe records. After being clustered by station and time period, the total number of data is 3 million. The process of cleaning the IC card data is to remove the data with empty boarding or alighting time, and to delete the data with an interval of more than 3 h from boarding to alighting time. The cleaned data account for about 1% of the total data. POI is a term in GIS which refers to all geographical objects that can be abstracted as points, especially some geographical entities that are closely related to people’s life, such as schools, banks, restaurants, gas stations, hospitals and supermarkets. The main use of POI is to describe the address of things or events, and the number of different types of POI in a region can characterize the attributes of the region. In this study, POI data collection around bus stops was carried out based on the Amap application programming interface (API). The API refers to a series of functions that have been predeﬁned. Developers can implement existing functions by calling API functions without accessing the source code or understanding the details of internal working mechanisms. The Amap location based services (LBS) open platform provides professional electronic maps and location services to the public. When developers integrate the corresponding software development kit (SDK), Appl. Sci. 2022, 12, 940 4 of 14 the interface can be invoked to implement many functions, such as map display, label POI, location retrieval, data storage and analysis. The collection process is divided into four parts: acquiring global positioning system (GPS) latitude and longitude of each station based on bus operation data, converting GPS latitude and longitude into Amap coordinates, collecting POI information based on Amap coordinates and organizing POI data into corresponding ﬁelds. To convert GPS coordinates to Amap coordinates, we need to apply the coordinate conversion method and add the corresponding parameters to the URL of the GET request. The main parameters for applying this method are listed in Table 1. Table 1. Coordinate conversion and peripheral searching parameters using Amap API. Parameter Meaning key Users apply for API types on the ofﬁcial website of AMap. Longitude and latitude are divided by “,”. Longitude is the location former and latitude is the latter. The decimal point of latitude and longitude should not exceed 6 digits. coordsys The original coordinate system. POI types. The classiﬁcation code consists of six digits. The ﬁrst types two numbers represent large categories, the middle two represent medium categories and the last two represent small categories. city City of inquiry. radius Radius of the inquiry. The value range is from 0 to 50,000. Output Return to data format type. 3.2. Passenger Flow Prediction Model We propose the PFP-XPOI model for passenger ﬂow prediction. The features selected for this model comprise the following three dimensions. One dimension is the information related to the line and the station, such as the line code of the station and the latitude and longitude of the station. Another dimension is the time period and the date when the IC card data are generated. The third dimension is the number of different types of POI around the station, including the number of companies and research institutions, etc. This model consists of two parts. One part is the calibration of the service radius between the bus station and POI data, and the other part is the training of the passenger ﬂow prediction model for each line. We built the PFP-XPOI model based on the following steps. The dataset D is a sample space, and we can represent the machine learning model as M(x 2 D ) ! y. (1) where M means a mapping from data point x to its true value y. After taking POI into account, we can add a new dataset to the original one. Namely D = f (D , D ). (2) n dis S P where D is the updated sample space. D means the POI data set. f refers to a distance- n P dis based function between bus stations and POI. In this model, distances were set to 100, 200, 300, 400 and 500 m, forming 5 datasets. After that, to obtain the optimal service radius d*, the machine learning model for different datasets was trained. Finally, d* can help us ﬁnd the best dataset. We trained a passenger ﬂow prediction model for each line based on this dataset using XGBoost. The detail of the PFP-XPOI model is shown in Figure 1. Appl. Sci. 2022, 12, x FOR PEER REVIEW 5 of 14 100, 200, 300, 400 and 500 m, forming 5 datasets. After that, to obtain the optimal service radius d*, the machine learning model for different datasets was trained. Finally, d* can Appl. Sci. 2022, 12, 940 help us find the best dataset. We trained a passenger flow prediction model for each line 5 of 14 based on this dataset using XGBoost. The detail of the PFP-XPOI model is shown in Figure Figure 1. The process and organization of the PFP-XPOI model. Figure 1. The process and organization of the PFP-XPOI model. 3.3. Model Training 3.3. Model Training In this research, XGBoost was used to train the model for every bus line. XGBoost is In this research, XGBoost was used to train the model for every bus line. XGBoost scalable in a wide range of situations because of the optimization of some important algo- is scalable in a wide range of situations because of the optimization of some important rithms and systems, including a novel tree learning algorithm for handling sparse data algorithms and systems, including a novel tree learning algorithm for handling sparse and a rational weighted quantile sketch process for controlling instance weights in ap- data and a rational weighted quantile sketch process for controlling instance weights in proximate tree learning. Its operating time is 10 times faster than other popular programs approximate tree learning. Its operating time is 10 times faster than other popular programs on a single device, and it scales up to billions of examples in the case of distributed or on a single device, and it scales up to billions of examples in the case of distributed or limited limited memory. Parallel and distributed computing makes learning faster which enables memory. Parallel and distributed computing makes learning faster which enables quicker quicker model exploration. In addition, utilization of out-of-core calculation enables hun- model exploration. In addition, utilization of out-of-core calculation enables hundred dred millions of examples to be processed on a desktop. These techniques can be con- millions of examples to be processed on a desktop. These techniques can be connected to nected to create an end-to-end system that extends to big data with the fewest cluster cr resourc eate an es.end-to-end system that extends to big data with the fewest cluster resources. XGBoost is one kind of boosting tree model aiming to generate certain tree models XGBoost is one kind of boosting tree model aiming to generate certain tree models for prediction. The tree ensemble model includes independent variable 𝑥 and dependent for prediction. The tree ensemble model includes independent variable 𝑖 x and dependent variable y and estimates the target value y using T additive functions. The function can be expressed as y = f(x ) = f (x ) (3) i å t i t=1 where y is the target value; y is the dependent variable (y is 1 if the passenger boards on i i or alights from the bus; otherwise, it is 0); x is the independent variable; t is the features; f (x ) is the model at the tth iteration and T is the number of tree functions. t i (t) The objective is to minimize the loss function L at the tth iteration which can be expressed as n (t1) (t) L = l y , y + f (x ) + W( f ) (4) t t å i i i=1 Appl. Sci. 2022, 12, 940 6 of 14 (t1) where l represents the loss function and y means the predicted value of the (t 1)th iteration. The additional term W( f ) plays a role in reducing the complexity of the model. (t1) (t) Approximating L with a second-order Taylor expansion for l y , y + f (x ) at i i (t1) y , the Equation (4) becomes (t1) (t) 2 L ' [l y , y ) + g f (x ) + h f (x )] + W( f ) (5) å i i t i i i t i=1 i (t1) (t1) ¶l y ,y ¶ l y ,y i i i i where g = , h = . i i (t1) (t1) ¶y ¶y i i (t1) l y , y in Equation (5) can be disregarded as it is a constant term. Therefore, we obtain a new simpliﬁed objective function as follows. n 1 (t) 2 L = [g f (x ) + h f (x )] + W( f ) (6) å i t i i i t i=1 For a tree structure, the samples can be grouped according to the leaf node, and the samples that fall into the same leaf node can be represented as I = i x 2 j . j is the f j g j i leaf node number. By introducing w as the score of leaf j, we can rewrite Equation (6) as follows. n 1 1 T (t) 2 2 L = [g f (x ) + h f (x )] + gT + l w å å i t i i i i=1 t j=1 2 2 j T (7) T 1 2 = l [ g w + h + l w ] + gT å å å å i2I i j i2I i j=1 2 j j j j=1 where g controls the number of leaf nodes and l prevents overﬁtting. Let the value of the ﬁrst-order partial derivative function of y concerning x be equal to 0, and then the optimal weight w of leaf j can be calculated as w = (8) H + l (t) L can ﬁnally be shown in Equation (9). 1 T G (t) L = + gT (9) j=1 2 H + l Normally it is impossible to enumerate all the possible tree structures. A greedy algorithm that starts from a single leaf and iteratively adds branches to the tree is used instead. Assume that I and I are the instance sets of left and right nodes after the split. L R Let I = I [ I , and then the loss reduction after the split is given by L R 1 G G G L R L = + g. (10) spilt 2 H + l H + l H + l L R With the help of the process above, we can calculate a tree for prediction. 4. Results and Discussion 4.1. Peak Period Experiments The training dataset used was extracted from 8 October 2015 to 25 October 2015. The test dataset is from 26 October 2015 to 30 October 2015. The two lines are 685 and 56008. Line 56008 has a large passenger volume because it is a major bus line on the third ring road in Beijing. Line 685 is a normal line that has a relatively small passenger volume. If the passenger numbers of the two lines are very large, the departure frequency will be relatively high; thus, we do not need to consider the transfer situation. If the passenger numbers of both lines are small, the number of passengers who need to transfer between Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 14 4. Results and Discussion 4.1. Peak Period Experiments The training dataset used was extracted from 8 October 2015 to 25 October 2015. The test dataset is from 26 October 2015 to 30 October 2015. The two lines are 685 and 56008. Line 56008 has a large passenger volume because it is a major bus line on the third ring road in Beijing. Line 685 is a normal line that has a relatively small passenger volume. If the passenger numbers of the two lines are very large, the departure frequency will be relatively high; thus, we do not need to consider the transfer situation. If the passenger Appl. Sci. 2022, 12, 940 7 of 14 numbers of both lines are small, the number of passengers who need to transfer between lines will be much smaller, so there is little need to consider the transfer coordination. Therefore, after calculation, we chose these two lines as our experimental lines. These two lines will be much smaller, so there is little need to consider the transfer coordination. lines can be transferred at Fangzhuangqiaoxi bus station. Therefore, after calculation, we chose these two lines as our experimental lines. These two With a Windows 10 operating system, a I7-8700k processor, and 32 GB memory, the lines can be transferred at Fangzhuangqiaoxi bus station. PFP-XPOI model takes 20 min to finish the process of determining the station query radius With a Windows 10 operating system, a I7-8700k processor, and 32 GB memory, the totally, and the process is executed only once after the general rule is obtained. In the PFP-XPOI model takes 20 min to ﬁnish the process of determining the station query radius process of passenger flow prediction, the total time for training a single-route passenger totally, and the process is executed only once after the general rule is obtained. In the flow prediction model is 4 min, while training a single-route CART model and a model process of passenger ﬂow prediction, the total time for training a single-route passenger such as SVM takes about 8 min, and the recurrent neural network (RNN) method with ﬂow prediction model is 4 min, while training a single-route CART model and a model seven steps takes about 6 h. such as SVM takes about 8 min, and the recurrent neural network (RNN) method with The root mean square error (RMSE) was selected to evaluate the model. The RMSE seven steps takes about 6 h. can be calculated by Equation (11). The root mean square error (RMSE) was selected to evaluate the model. The RMSE can be calculated by Equation (11). √ (11) | | RMSE = ∑ 𝑦 − 𝑦 ̂ 𝑚 𝑚 𝑚 =1 RMSE = y y ˆ (11) j j å m m m=1 where 𝑀 is the total number of samples. 𝑦 is the true value, and 𝑦 ̂ is the predicted 𝑚 𝑚 value. where M is the total number of samples. y is the true value, and y ˆ is the predicted value. m m For line 56008, the optimal parameters of the predicted model are as follows. The For line 56008, the optimal parameters of the predicted model are as follows. The maximum tree depth is four layers. The learning rate is 0.02. The maximum tree size is maximum tree depth is four layers. The learning rate is 0.02. The maximum tree size is 1500, and the optimal distance is 300 m. For line 685, the optimal parameters of the model 1500, and the optimal distance is 300 m. For line 685, the optimal parameters of the model are as follows. The maximum tree depth is three layers. The learning rate is 0.01. The max- are as follows. The maximum tree depth is three layers. The learning rate is 0.01. The imum size of the tree is 800, and the optimal distance is 300 m. The evaluation of the pre- maximum size of the tree is 800, and the optimal distance is 300 m. The evaluation of the diction model for lines 56008 and 685 under different distances is shown in Figure 2. prediction model for lines 56008 and 685 under different distances is shown in Figure 2. Figure Figure 2. 2. The The R RMSE MSE and and distance distance of of passenger passenger num number ber pr pre ediction diction model in model in lines lines56008 56008 and and 685. 685. For line 56008, the ﬁgure reﬂects that the RMSE value of the test set reaches the For line 56008, the figure reflects that the RMSE value of the test set reaches the min- minimum at a distance of 300 m, namely where the error of the prediction model is the imum at a distance of 300 m, namely where the error of the prediction model is the small- smallest, about 7.7. When the distance is 500 and 100 m, the RMSE is lager. Similarly, est, about 7.7. When the distance is 500 and 100 m, the RMSE is lager. Similarly, for line for line 685, the minimum of RSME value is also found at a distance of 300 m, about 4.9. 685, the minimum of RSME value is also found at a distance of 300 m, about 4.9. However, However, the effect of different distances on the accuracy of the model in line 685 is smaller than that in line 56008. The results suggest that grouping the data by lines and training one model for each line can reduce the interference between different lines and effectively reduce the prediction error. We divided the early peak period into four sections with an interval of 30 min. Taking samples on 28 October 2015 as an example, the predicted values and true values of on-board and alighting passenger numbers of line 56008 are shown in Figures 3 and 4, respectively. Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 of 14 Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 of 14 the effect of different distances on the accuracy of the model in line 685 is smaller than the effect of different distances on the accuracy of the model in line 685 is smaller than that in line 56008. The results suggest that grouping the data by lines and training one that in line 56008. The results suggest that grouping the data by lines and training one model for each line can reduce the interference between different lines and effectively re- model for each line can reduce the interference between different lines and effectively re- duce the prediction error. duce the prediction error. We divided the early peak period into four sections with an interval of 30 min. Taking We divided the early peak period into four sections with an interval of 30 min. Taking samples on 28 October 2015 as an example, the predicted values and true values of on- Appl. Sci. 2022, 12, 940 8 of 14 samples on 28 October 2015 as an example, the predicted values and true values of on- board and alighting passenger numbers of line 56008 are shown in Figures 3 and 4, re- board and alighting passenger numbers of line 56008 are shown in Figures 3 and 4, re- spectively. spectively. Figure 3. Prediction and true values of on-board passenger number for line 56008. Figure 3. Prediction and true values of on-board passenger number for line 56008. Figure 3. Prediction and true values of on-board passenger number for line 56008. Figure 4. Prediction and true values of alighting passenger number for line 56008. The number of passengers boarding from 7:00 to 8:00 on line 56008 was signiﬁcantly greater than that from 8:00 to 9:00. There were two main boarding stations for line 56008, namely stations 6 and 16. The peak boarding passenger ﬂow on line 56008 was about 230. Compared with on-board passengers, the distribution of alighting passengers between 7:00 to 8:00 and 8:00 to 9:00 was more balanced, and the total number of alighting passengers was not obviously different between the two periods. However, from 7:00 to 8:00, the stations where passengers alighted were more concentrated. Stations 8 and 22 were the two main drop-off stations of line 56008. The peak alighting ﬂow of line 56008 was about 240. Appl. Sci. 2022, 12, x FOR PEER REVIEW 9 of 14 Figure 4. Prediction and true values of alighting passenger number for line 56008. The number of passengers boarding from 7:00 to 8:00 on line 56008 was significantly greater than that from 8:00 to 9:00. There were two main boarding stations for line 56008, namely stations 6 and 16. The peak boarding passenger flow on line 56008 was about 230. Compared with on-board passengers, the distribution of alighting passengers between 7:00 to 8:00 and 8:00 to 9:00 was more balanced, and the total number of alighting passen- Appl. Sci. 2022, 12, 940 9 of 14 gers was not obviously different between the two periods. However, from 7:00 to 8:00, the stations where passengers alighted were more concentrated. Stations 8 and 22 were the two main drop-off stations of line 56008. The peak alighting flow of line 56008 was about In comparison with line 56008, the passenger ﬂow of line 685 had decreased signif- In comparison with line 56008, the passenger flow of line 685 had decreased signifi- icantly. The on-board passenger ﬂow from 8:00 to 9:00 was greater than that from 7:00 cantly. The on-board passenger flow from 8:00 to 9:00 was greater than that from 7:00 to to 8:00. During the two periods, stations 1 to 5 were the main pick-up stations, and the 8:00. During the two periods, stations 1 to 5 were the main pick-up stations, and the peak peak passenger ﬂow for boarding was about 50. Stations 6 and 9 were the main drop-off passenger flow for boarding was about 50. Stations 6 and 9 were the main drop-off sta- stations. Station 6 was the transfer station of Lines 685 and 56008, so a group of passengers tions. Station 6 was the transfer station of Lines 685 and 56008, so a group of passengers chose to get off at this station. The peak alighting ﬂow was about 60. The details of the chose to get off at this station. The peak alighting flow was about 60. The details of the predicted values and the real values for on-board and alighting passengers are shown in predicted values and the real values for on-board and alighting passengers are shown in Figur Figure es s 55 an and d 6, respect 6, respectively ively. . Appl. Sci. 2022, 12, x FOR PEER REVIEW 10 of 14 Figure 5. Prediction and true values of on-board passenger numbers for line 685. Figure 5. Prediction and true values of on-board passenger numbers for line 685. Figure Figure 6. 6. Predi Prediction ction and and tru tr e values ue values of al of ighting alighting passeng passenger er number numbers s for line 685 for line . 685. 4.2. Impact Analysis of POI There were 23 specific features selected in the PFP-XPOI model for passenger flow forecasting, and the feature importance is shown in Figure 7. Figure 7. The feature importance of different XGBoost models with POI data (a) and without POI data (b). The times of node split were used as the feature importance in the XGBoost algo- rithm. The more times a feature splits, the more important it is. Figure 7 shows the feature Appl. Sci. 2022, 12, x FOR PEER REVIEW 10 of 14 Figure 6. Prediction and true values of alighting passenger numbers for line 685. Appl. Sci. 2022, 12, 940 10 of 14 4.2. Impact Analysis of POI There were 23 specific features selected in the PFP-XPOI model for passenger flow 4.2. Impact Analysis of POI forecasting, and the feature importance is shown in Figure 7. There were 23 speciﬁc features selected in the PFP-XPOI model for passenger ﬂow forecasting, and the feature importance is shown in Figure 7. Figure 7. The feature importance of different XGBoost models with POI data (a) and without POI data (b). Figure 7. The feature importance of different XGBoost models with POI data (a) and without POI data (b). The times of node split were used as the feature importance in the XGBoost algorithm. The more times a feature splits, the more important it is. Figure 7 shows the feature impor- The times of node split were used as the feature importance in the XGBoost algo- tance of different models. PFP-XPOI uses the XGBoost algorithm to train the passenger ﬂow rithm. The more times a feature splits, the more important it is. Figure 7 shows the feature prediction model. After the POI data are fused, the feature importance of the model will change signiﬁcantly. When POI data are not used, the model mainly splits by the station index, which makes this feature signiﬁcant in the split process. In the case of modeling with POI data, the model splits more evenly at different features. The effect of the POI data on the passenger ﬂow prediction for line 56008 is described directly in Figures 8 and 9. They illustrate the predicted values of on-board and alighting passenger number from 7:00 to 7:30 on 29 October 2015. The predicted values of XGBoost and the historical average model are almost the same. According to this phenomenon, we can draw conclusions in accordance with the results shown in Figure 7. The major split point of the XGBoost model is the index of stations. After the calibration of the service radius between bus stations and POI data, the PFP-XPOI model has a better performance than other models in passenger ﬂow prediction. 4.3. Comparison with Multiple Models To verify the accuracy of the PFP-XPOI model, this study compared the performance of different models as listed in Tables 2–5. We used the RMSE, mean absolute error (MAE) and R-squared to evaluate different models. The MAE can be expressed as 1 M MAE = jy y ˆ j (12) å m m m=1 where M is the total number of samples. y is the true value, and y ˆ is the predicted value. m m R-squared can be expressed as å (y y ˆ ) m m m=1 R squared = 1 (13) M 2 y y å ( ) m=1 m Appl. Sci. 2022, 12, x FOR PEER REVIEW 11 of 14 importance of different models. PFP-XPOI uses the XGBoost algorithm to train the pas- senger flow prediction model. After the POI data are fused, the feature importance of the model will change significantly. When POI data are not used, the model mainly splits by the station index, which makes this feature significant in the split process. In the case of modeling with POI data, the model splits more evenly at different features. The effect of the POI data on the passenger flow prediction for line 56008 is described directly in Figures 8 and 9. They illustrate the predicted values of on-board and alighting passenger number from 7:00 to 7:30 on 29 October 2015. The predicted values of XGBoost Appl. Sci. 2022, 12, 940 11 of 14 and the historical average model are almost the same. According to this phenomenon, we can draw conclusions in accordance with the results shown in Figure 7. The major split point of the XGBoost model is the index of stations. After the calibration of the service where M is the total number of samples. y is the true value. y ˆ is the predicted value, and radius between bus stations and POI data, the m PFP-XPOI model hasm a better performance y is the mean of samples. than other models in passenger flow prediction. Appl. Sci. 2022, 12, x FOR PEER REVIEW 12 of 14 Figure 8. Predicted and true values of on-board passenger numbers using three models. Figure 8. Predicted and true values of on-board passenger numbers using three models. Figure 9. Predicted and true values of alighting passenger numbers using three models. Figure 9. Predicted and true values of alighting passenger numbers using three models. 4.3. Comparison with Multiple Models To verify the accuracy of the PFP-XPOI model, this study compared the performance of different models as listed in Tables 2–5. We used the RMSE, mean absolute error (MAE) and R-squared to evaluate different models. The MAE can be expressed as MAE = ∑ |𝑦 − 𝑦 ̂ | (12) 𝑚 𝑚 𝑚 =1 where 𝑀 is the total number of samples. 𝑦 is the true value, and 𝑦 ̂ is the predicted 𝑚 𝑚 value. R-squared can be expressed as 𝑀 2 (𝑦 − 𝑦 ̂ ) 𝑚 =1 𝑚 𝑚 R − squared = 1 − (13) 𝑀 2 ∑ (𝑦 − 𝑦 ̅ ) 𝑚 𝑚 𝑚 =1 where 𝑀 is the total number of samples. 𝑦 is the true value. 𝑦 ̂ is the predicted value, 𝑚 𝑚 and 𝑦 ̅ is the mean of samples. Table 2. Evaluation values of different models for on-board passenger prediction in line 56008. On-Board Passenger Prediction Models in Line 56008 RMSE MAE R-Squared PFP-XPOI 7.84 7.32 0.912 XGBoost 8.79 8.16 0.889 LSTM 8.69 8.12 0.892 SVM 8.89 8.25 0.887 Historical Average 8.96 8.34 0.885 Table 3. Evaluation values of different models for alighting passenger prediction in line 56008. Alighting Passenger Prediction Models in Line 56008 RMSE MAE R-Squared PFP-XPOI 7.43 6.98 0.931 XGBoost 8.06 7.52 0.919 LSTM 7.49 7.13 0.929 SVM 7.96 7.48 0.921 Historical Average 8.12 7.65 0.917 Appl. Sci. 2022, 12, 940 12 of 14 Table 2. Evaluation values of different models for on-board passenger prediction in line 56008. On-Board Passenger Prediction Models in RMSE MAE R-Squared Line 56008 PFP-XPOI 7.84 7.32 0.912 XGBoost 8.79 8.16 0.889 LSTM 8.69 8.12 0.892 SVM 8.89 8.25 0.887 Historical Average 8.96 8.34 0.885 Table 3. Evaluation values of different models for alighting passenger prediction in line 56008. Alighting Passenger Prediction Models in RMSE MAE R-Squared Line 56008 PFP-XPOI 7.43 6.98 0.931 XGBoost 8.06 7.52 0.919 LSTM 7.49 7.13 0.929 SVM 7.96 7.48 0.921 Historical Average 8.12 7.65 0.917 Table 4. Evaluation values of different models for on-board passenger prediction in line 685. On-Board Passenger Prediction Models in RMSE MAE R-Squared Line 685 PFP-XPOI 4.92 4.53 0.890 XGBoost 5.76 4.74 0.849 LSTM 5.32 4.66 0.871 SVM 6.09 4.90 0.831 Historical Average 5.53 4.92 0.861 Table 5. Evaluation values of different models for alighting passenger prediction in line 685. Alighting Passenger Prediction Models in RMSE MAE R-Squared Line 685 PFP-XPOI 4.73 4.34 0.925 XGBoost 5.48 5.02 0.899 LSTM 5.13 4.97 0.912 SVM 5.53 5.12 0.898 Historical Average 5.69 5.14 0.892 Results reveal that the PFP-XPOI performs best, followed by LSTM and XGBoost. This phenomenon is similar to that obtained by Spyros Makridakis [16]. Because the alighting passenger ﬂow is more stable, the alighting passenger ﬂow prediction model is more accurate than the on-board passenger ﬂow prediction model for both lines. The results demonstrate that the PFP-XPOI model performs better in prediction and improves the prediction accuracy due to the addition of new features. The historical average data cannot effectively take the impact of week, POI and other factors into account so the error is relatively large. The error of using XGBoost model individually is similar to that of the historical mean. This also indicates that the direct application of XGBoost model for passenger ﬂow prediction is mainly based on the station index. 5. Conclusions Based on IC card data of Beijing buses, this study addressed the bus passenger ﬂow prediction problem via fusing POI data by using the XGBoost algorithm. The proposed Appl. Sci. 2022, 12, 940 13 of 14 method takes advantage of the accuracy ensured by POI generated from bus operation data and the efﬁciency guaranteed by the XGBoost algorithm. Through the XGBoost algorithm, the big data of the bus card can be merged with the POI data. After calculating the experimental data, we chose “300 m” as the query radius because the prediction outcome is the most accurate. Due to some new added features, the PFP-XPOI model can improve the dimension of smart card data by fusing the POI data. By comparison and veriﬁcation, it was proved that the proposed model has higher accuracy and runs faster. This work may be further strengthened in other ﬁelds. The modeling of multiple buses arriving and leaving a single bus station would require more in-depth analysis. In the future, we will explore the applications of the proposed method in intelligent transportation system comprehensively. Author Contributions: Data curation, W.L. and Y.R.; Formal analysis, Q.O.; Investigation, W.L. and Q.O.; Methodology, W.L.; Supervision, Y.L.; Writing—original draft, W.L.; Writing—review and editing, W.L. and Y.R. All authors have read and agreed to the published version of the manuscript. Funding: This research is supported by the National Natural Science Foundation of China (61872036). Data Availability Statement: The data is available through a partnership with BPTC and is not publicly available. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Beijing Public Transport Corporation. Available online: http://www.bjbus.com/home/index.php (accessed on 23 December 2021). 2. Pelletier, M.P.; Trepanier, M.; Morency, C. Smart card data use in public transit: A literature review. Transp. Res. C-Emerg. 2011, 19, 557–568. [CrossRef] 3. Noekel, K.; Viti, F.; Rodriguez, A.; Hernandez, S. 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Applied Sciences – Multidisciplinary Digital Publishing Institute

Published: Jan 18, 2022

Keywords: public transportation; passenger flow prediction; point-of-interest data; extreme gradient boosting algorithm

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A Bus Passenger Flow Prediction Model Fused with Point-of-Interest Data Based on Extreme Gradient Boosting

A Bus Passenger Flow Prediction Model Fused with Point-of-Interest Data Based on Extreme Gradient Boosting

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A Bus Passenger Flow Prediction Model Fused with Point-of-Interest Data Based on Extreme Gradient Boosting

A Bus Passenger Flow Prediction Model Fused with Point-of-Interest Data Based on Extreme Gradient Boosting

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