Subgraph Matching Kernels for Attributed Graphs

We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by a exible scoring scheme comparing vertex and edge attributes by kernels. We show that subgraph matching kernels generalize several known kernels. To compute the kernel we propose a graph-theoretical algorithm inspired by a classical relation between common subgraphs of two graphs and cliques in their product graph observed by Levi (1973). Encouraging experimental results on a classification task of real-world graphs are presented.

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

[2]  G. Levi.  A note on the derivation of maximal common subgraphs of two directed or undirected graphs , 1973 .

[3]  Tatsuya Akutsu,et al.  Extensions of marginalized graph kernels , 2004, ICML.

[4]  Jean-Philippe Vert,et al.  Graph kernels based on tree patterns for molecules , 2006, Machine Learning.

[5]  Kurt Mehlhorn,et al.  Weisfeiler-Lehman Graph Kernels , 2011, J. Mach. Learn. Res..

[6]  S. V. N. Vishwanathan,et al.  Graph kernels , 2007 .

[7]  Jean-Philippe Vert,et al.  The Pharmacophore Kernel for Virtual Screening with Support Vector Machines , 2006, J. Chem. Inf. Model..

[8]  Paolo Frasconi,et al.  Weighted decomposition kernels , 2005, ICML.

[9]  Kurt Mehlhorn,et al.  Efficient graphlet kernels for large graph comparison , 2009, AISTATS.

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

[11]  Hisashi Kashima,et al.  Marginalized Kernels Between Labeled Graphs , 2003, ICML.

[12]  Hans-Peter Kriegel,et al.  Shortest-path kernels on graphs , 2005, Fifth IEEE International Conference on Data Mining (ICDM'05).

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

[14]  Zaïd Harchaoui,et al.  Image Classification with Segmentation Graph Kernels , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

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

[16]  Andreas Zell,et al.  Optimal assignment kernels for attributed molecular graphs , 2005, ICML.

[17]  George Karypis,et al.  Comparison of descriptor spaces for chemical compound retrieval and classification , 2006, Sixth International Conference on Data Mining (ICDM'06).

[18]  Ina Koch,et al.  Enumerating all connected maximal common subgraphs in two graphs , 2001, Theor. Comput. Sci..

[19]  Fabrizio Costa,et al.  Fast Neighborhood Subgraph Pairwise Distance Kernel , 2010, ICML.