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M. Meilă, Michael Jordan (2001)
Learning with Mixtures of TreesJ. Mach. Learn. Res., 1
M. Collins, Nigel Duffy (2001)
Convolution Kernels for Natural Language
Chih-Chung Chang, Chih-Jen Lin (2011)
LIBSVM: A library for support vector machinesACM Trans. Intell. Syst. Technol., 2
C. Berg, J. Christensen, P. Ressel (1984)
Harmonic Analysis on Semigroups
Sara Cohen, Nerya Or (2014)
A general algorithm for subtree similarity-search2014 IEEE 30th International Conference on Data Engineering
K. Hashimoto, S. Goto, S. Kawano, Kiyoko Aoki-Kinoshita, Nobuhisa Ueda, Masami Hamajima, Toshisuke Kawasaki, M. Kanehisa (2006)
KEGG as a glycome informatics resource.Glycobiology, 16 5
K. Tai (1979)
The Tree-to-Tree Correction ProblemJ. ACM, 26
Mohammed Zaki, C. Aggarwal (2006)
XRules: An effective algorithm for structural classification of XML dataMachine Learning, 62
Kaizhong Zhang (1995)
Algorithms for the constrained editing distance between ordered labeled trees and related problemsPattern Recognit., 28
G. Hommel (1988)
A stagewise rejective multiple test procedure based on a modified Bonferroni testBiometrika, 75
M. Neuhaus, H. Bunke (2006)
Edit distance-based kernel functions for structural pattern classificationPattern Recognit., 39
D. Haussler (1999)
Convolution Kernels on Discrete Structures UCSC CRL
P. Klein (1998)
Computing the Edit-Distance between Unrooted Ordered Trees
Example data for TREE KERNELS IN SVM-LIGHT. http://disi.unitn.it/moschitti/ Tree-Kernel
T. Kuboyama, Kilho Shin, T. Miyahara, H. Yasuda (2005)
A Theoretical Analysis of Alignment and Edit Problems for Trees
E. Demaine, S. Mozes, Benjamin Rossman, O. Weimann (2006)
An optimal decomposition algorithm for tree edit distanceACM Trans. Algorithms, 6
S. García, F. Herrera (2008)
An Extension on "Statistical Comparisons of Classifiers over Multiple Data Sets" for all Pairwise ComparisonsJournal of Machine Learning Research, 9
Kilho Shin, T. Kuboyama (2008)
A Generalization of Haussler's Convolution Kernel — Mapping Kernel and Its Application to Tree KernelsJournal of Computer Science and Technology, 25
Thomas Gärtner (2003)
A survey of kernels for structured dataSIGKDD Explor., 5
HFS Garcia (2008)
An extension on Statistical comparisons of classifiers over multiple data sets for all pairwise comparisonsJ. Mach. Learn. Theory, 9
Kilho Shin, Marco Cuturi, T. Kuboyama (2011)
Mapping kernels for trees
M. Garofalakis, Amit Kumar (2005)
XML stream processing using tree-edit distance embeddingsACM Trans. Database Syst., 30
P. Bille (2005)
A survey on tree edit distance and related problemsTheor. Comput. Sci., 337
Kilho Shin (2015)
Tree Edit Distance and Maximum Agreement SubtreeInf. Process. Lett., 115
Shin-Yee Lu (1979)
A Tree-to-Tree Distance and Its Application to Cluster AnalysisIEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-1
Tao Jiang, Lusheng Wang, Kaizhong Zhang (1994)
Alignment of Trees - An Alternative to Tree Edit
S. Dulucq, H. Touzet (2003)
Analysis of Tree Edit Distance Algorithms
H. Bunke (1997)
On a relation between graph edit distance and maximum common subgraphPattern Recognit. Lett., 18
Mateusz Pawlik, Nikolaus Augsten (2011)
RTED: A Robust Algorithm for the Tree Edit DistanceArXiv, abs/1201.0230
P. Marteau, S. Gibet (2010)
On Recursive Edit Distance Kernels With Application to Time Series ClassificationIEEE Transactions on Neural Networks and Learning Systems, 26
B. Scholkopf (2000)
The Kernel Trick for Distances
I. Schoenberg (1938)
Metric spaces and positive definite functionsTransactions of the American Mathematical Society, 44
M. Neuhaus, H. Bunke (2007)
Bridging the Gap between Graph Edit Distance and Kernel Machines, 68
J. Demšar (2006)
Statistical Comparisons of Classifiers over Multiple Data SetsJ. Mach. Learn. Res., 7
T. Kuboyama, Kilho Shin, H. Kashima (2006)
Flexible Tree Kernels based on Counting the Number of Tree Mappings
Thorsten Richter (1997)
A New Measure of the Distance between Ordered Trees and its Applications
哲二 久保山 (2007)
Matching and learning in trees
R. Wagner, M. Fischer (1974)
The String-to-String Correction ProblemJ. ACM, 21
Corinna Cortes, P. Haffner, M. Mohri (2004)
Rational Kernels: Theory and AlgorithmsJ. Mach. Learn. Res., 5
H. Kashima, Teruo Koyanagi (2002)
Kernels for Semi-Structured Data
Nikolaus Augsten, Michael Böhlen, C. Dyreson, J. Gamper (2012)
Windowed pq-grams for approximate joins of data-centric XMLThe VLDB Journal, 21
(1995)
Tree-to-tree correction for document trees, technical report 95-375
Nikolaus Augsten, Michael Böhlen, J. Gamper (2010)
The pq-gram distance between ordered labeled treesACM Trans. Database Syst., 35
D. Haussler (1999)
Convolution kernels on discrete structures
C. Lu, Z. Su, C. Tang (2001)
A New Measure of Edit Distance between Labeled Trees
Kaizhong Zhang, D. Shasha (1989)
Simple Fast Algorithms for the Editing Distance Between Trees and Related ProblemsSIAM J. Comput., 18
C. Berg, J. Christensen, P. Ressel (1984)
Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
J. Wang, Kaizhong Zhang (2001)
Finding similar consensus between trees: an algorithm and a distance hierarchyPattern Recognit., 34
Kaspar Riesen, H. Bunke (2009)
Graph Classification by Means of Lipschitz EmbeddingIEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 39
E. Demaine, S. Mozes, Benjamin Rossman, O. Weimann (2006)
An O(n^3)-Time Algorithm for Tree Edit DistanceArXiv, abs/cs/0604037
Edit distances provide us with an established method to capture structural features of data, and a distance between data objects represents their dissimilarity. In contrast, kernels form a category of similarity functions, and a positive definite kernel enables us to leverage abundant techniques of multivariate analysis. This paper aims to fill the gap between distances and kernels. In the literature, we have several formulas that convert a negative definite distance function into a positive definite kernel. Edit distance functions, however, are not necessarily negative definite, and our first contribution is to introduce an alternative method to derive positive definite kernels from edit distance functions that are not necessarily negative definite. The method is equipped with an easy-to-check and strong sufficient condition for positive definiteness, and the condition turns out to be tightly related with the triangle inequality. In fact, to our knowledge, all of the edit distance functions in the literature that support the triangle inequality meet the condition for positive definiteness. Secondly, we apply this method to four well-known edit distance functions for trees to introduce four novel kernels and show that three of them are positive definite. Thirdly, we develop a theory of subtree matching to study these kernels. Our kernels count matchings between subtrees of the input trees with weights determined according to individual matchings. Although the number of such matchings is an exponential function of the size of the input trees (the number of vertices), our theory enables us to develop dynamic-programming-based algorithms, whose asymptotic computational complexities fall between a quadratic function and a cubic function of the size.
Annals of Mathematics and Artificial Intelligence – Springer Journals
Published: Jul 19, 2015
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