A Family of Novel Graph Kernels for Structural Pattern Recognition

Recently, an emerging trend of representing objects by graphs can be observed. As a matter of fact, graphs offer a versatile alternative to feature vectors in pattern recognition, machine learning and data mining. However, the space of graphs contains almost no mathematical structure, and consequently, there is a lack of suitable methods for graph classification. Graph kernels, a novel class of algorithms for pattern analysis, offer an elegant solution to this problem. Graph kernels aim at bridging the gap between statistical and symbolic object representations. In the present paper we propose a general approach to transforming graphs into n-dimensional real vector spaces by means of graph edit distance. As a matter of fact, this approach results in a novel family of graph kernels making a wide range of kernel machines applicable for graphs. With several experimental results we prove the robustness and flexibility of our new method and show that our approach outperforms a standard graph classification method on several graph data sets of diverse nature.

[1]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[2]  Jan Ramon,et al.  Expressivity versus efficiency of graph kernels , 2003 .

[3]  Thomas Gärtner,et al.  A survey of kernels for structured data , 2003, SKDD.

[4]  Kaspar Riesen,et al.  Reducing the Dimensionality of Vector Space Embeddings of Graphs , 2007, MLDM.

[5]  David G. Stork,et al.  Pattern Classification , 1973 .

[6]  Yoav Freund,et al.  A decision-theoretic generalization of on-line learning and an application to boosting , 1997, EuroCOLT.

[7]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[8]  Horst Bunke,et al.  A Graph Matching Based Approach to Fingerprint Classification Using Directional Variance , 2005, AVBPA.

[9]  Fritz Wysotzki,et al.  SVM learning with the Schur-Hadamard inner product for graphs , 2005, Neurocomputing.

[10]  Horst Bunke,et al.  Feature Selection for Graph-Based Image Classifiers , 2005, IbPRIA.

[11]  Hans-Peter Kriegel,et al.  Protein function prediction via graph kernels , 2005, ISMB.

[12]  Josef Kittler,et al.  Floating search methods in feature selection , 1994, Pattern Recognit. Lett..

[13]  David G. Stork,et al.  Pattern Classification (2nd ed.) , 1999 .

[14]  Subhash C. Bagui,et al.  Combining Pattern Classifiers: Methods and Algorithms , 2005, Technometrics.

[15]  Thomas Gärtner,et al.  Cyclic pattern kernels for predictive graph mining , 2004, KDD.

[16]  Horst Bunke,et al.  Inexact graph matching for structural pattern recognition , 1983, Pattern Recognit. Lett..

[17]  Richard C. Wilson,et al.  Levenshtein distance for graph spectral features , 2004, ICPR 2004.

[18]  Vladimir Vapnik,et al.  Chervonenkis: On the uniform convergence of relative frequencies of events to their probabilities , 1971 .

[19]  Tatsuya Akutsu,et al.  Graph Kernels for Molecular Structure-Activity Relationship Analysis with Support Vector Machines , 2005, J. Chem. Inf. Model..

[20]  Ludmila I. Kuncheva,et al.  Combining Pattern Classifiers: Methods and Algorithms , 2004 .

[21]  Horst Bunke,et al.  Bridging the Gap between Graph Edit Distance and Kernel Machines , 2007, Series in Machine Perception and Artificial Intelligence.

[22]  Kaspar Riesen,et al.  Fast Suboptimal Algorithms for the Computation of Graph Edit Distance , 2006, SSPR/SPR.

[23]  Edwin R. Hancock,et al.  Pattern Vectors from Algebraic Graph Theory , 2005, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Tin Kam Ho,et al.  The Random Subspace Method for Constructing Decision Forests , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  Kaspar Riesen,et al.  Classifier Ensembles for Vector Space Embedding of Graphs , 2007, MCS.

[26]  Kaspar Riesen,et al.  Graph Embedding in Vector Spaces by Means of Prototype Selection , 2007, GbRPR.

[27]  John D. Lafferty,et al.  Diffusion Kernels on Statistical Manifolds , 2005, J. Mach. Learn. Res..

[28]  Thomas Gärtner,et al.  On Graph Kernels: Hardness Results and Efficient Alternatives , 2003, COLT.

[29]  King-Sun Fu,et al.  A distance measure between attributed relational graphs for pattern recognition , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[30]  Robert P. W. Duin,et al.  The Dissimilarity Representation for Pattern Recognition - Foundations and Applications , 2005, Series in Machine Perception and Artificial Intelligence.

[31]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[32]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[33]  David Haussler,et al.  Convolution kernels on discrete structures , 1999 .

[34]  Josef Kittler,et al.  Audio- and Video-Based Biometric Person Authentication, 5th International Conference, AVBPA 2005, Hilton Rye Town, NY, USA, July 20-22, 2005, Proceedings , 2005, AVBPA.

[35]  Kaspar Riesen,et al.  Bipartite Graph Matching for Computing the Edit Distance of Graphs , 2007, GbRPR.

[36]  Bernhard Schölkopf,et al.  Learning with kernels , 2001 .

[37]  Edwin R. Hancock,et al.  Spectral embedding of graphs , 2003, Pattern Recognit..

[38]  Klaus Jansen,et al.  Experimental and Efficient Algorithms , 2003, Lecture Notes in Computer Science.