Abstract
Graph mining is of great interest because knowledge discovery from structured data can be applied to real-world datasets. Recent improvements in system throughput have led to the need for the analysis of a large number of graphs using methods such as graph classification, the objective of which is to classify graphs of similar structures into the same class. Existing methods for representing graphs can result in difficulties such as the loss of structural information, which can be overcome using specifically designed graph kernels. In this paper, we propose two novel graph kernels, mapping distance kernel with stars (MDKS) and mapping distance kernel with vectors (MDKV), to classify labeled graphs more accurately than existing methods. The MDKS is based on the graph edit distance using star structures, and the MDKV is based on the graph edit distance using the linear sum assignment problem and graph relabeling. Because MDKS uses only small local structures that consist of adjacent vertices of each vertex in graphs, it is not substantially superior to conventional graph kernels. However, the MDKV uses local structures that consist of vertices that are reachable within a small number of steps from each vertex in graphs and, unlike existing methods, do not require isomorphism matching. In addition, we investigate a framework for computing the approximate graph edit distance between two graphs using the linear sum assignment problem (LSAP), because the proposed graph kernels are related to methods for computing the graph edit distance using LSAP.
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Notes
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The figures and tables showing experimental results are the same as ones in the conference version of this paper [14].
References
Bach, F.R.: Graph kernels between point clouds. In: Proceedings of the International Conference on Machine Learning (ICML), pp. 25–32 (2008)
Borgwardt, K.M., Kriegel, H.-P.: Shortest-path kernels on graphs. In: Proceedings of IEEE International Conference on Data Mining (ICDM), pp. 74–81 (2005)
Carletti, V., Gaüzère, B., Brun, L., Vento, M.: Approximate graph edit distance computation combining bipartite matching and exact neighborhood substructure distance. In: Liu, C.-L., Luo, B., Kropatsch, W.G., Cheng, J. (eds.) GbRPR 2015. LNCS, vol. 9069, pp. 188–197. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-18224-7_19
Chang, C.-C., Lin, C.-J.: LIBSVM: A Library for Support Vector Machines (2001). http://www.csie.ntu.edu.tw/cjlin/libsvm
Costa, F., De Grave, K.: Fast neighborhood subgraph pairwise distance kernel. In: Proceedings of International Conference on Machine Learning (ICML), pp. 255–262 (2010)
Debnath, A.K., Lopez de Compadre, R.L., Debnath, G., Shusterman, A.J., Hansch, C.: Structure-activity relationship of mutagenic aromatic and heteroaromatic nitro compounds. Correlation with molecular orbital energies and hydrophobicity. J. Med. Chem. 34, 786–797 (1991)
Demaine, E.D., Mozes, S., Rossman, B., Weimann, O.: An optimal decomposition algorithm for tree edit distance. ACM Trans. Algorithm 6(1), 2:1–2:19 (2009)
Gärtner, T., Flach, P., Wrobel, S.: On graph kernels: hardness results and efficient alternatives. In: Schölkopf, B., Warmuth, M.K. (eds.) COLT-Kernel 2003. LNCS (LNAI), vol. 2777, pp. 129–143. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45167-9_11
Gaüzère, B., Bougleux, S., Riesen, K., Brun, L.: Approximate graph edit distance guided by bipartite matching of bags of walks. In: Fränti, P., Brown, G., Loog, M., Escolano, F., Pelillo, M. (eds.) S+SSPR 2014. LNCS, vol. 8621, pp. 73–82. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44415-3_8
Helma, C., Kramer, S.: A survey of the predictive toxicology challenge. Bioinformatics 19(10), 1179–1182 (2003)
Hido, S., Kashima, H.: A linear-time graph kernel. In: Proceedings of the International Conference on Data Mining (ICDM), pp. 179–188 (2009)
Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized kernels between labeled graphs. In: Proceedings of the International Conference on Machine Learning (ICML), pp. 321–328 (2003)
Kataoka, T., Inokuchi, A.: Hadamard code graph kernels for classifying graphs. In: Proceedings of the International Conference on Pattern Recognition Applications and Methods (ICPRAM), pp. 24–32 (2016)
Kataoka, T., Shiotsuki, E., Inokuchi, A.: Mapping distance graph kernels using bipartite matching. In: Proceedings of the International Conference on Pattern Recognition Applications and Methods (ICPRAM), pp. 61–70 (2017)
Koopmans, T.C., Beckmann, M.: Assignment problems and the location of economic activities. Econometrica 25(1), 53–76 (1957)
Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)
Haussler, D.: Convolution kernels on discrete structures. Technical report, UCSC-CRL-99-10, University of California at Santa Cruz (1999)
Horváth, T., Gärtner, T., Wrobel, S.: Cyclic pattern kernels for predictive graph mining. In: Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining, (KDD), pp. 158–167 (2004)
Inokuchi, A., Washio, T., Motoda, H.: An apriori-based algorithm for mining frequent substructures from graph data. In: Zighed, D.A., Komorowski, J., Żytkow, J. (eds.) PKDD 2000. LNCS (LNAI), vol. 1910, pp. 13–23. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45372-5_2
Kuhn, H.W.: The Hungarian method for the assignment problem. Nav. Res. Logist. 2, 83–97 (1955)
Neuhaus, M., Bunke, H.: Bridging the Gap Between Graph Edit Distance and Kernel Machines. World Scientific, Singapore (2007)
Mahé, P., Vert, J.-P.: Graph kernels based on tree patterns for molecules. Mach. Learn. 75(1), 3–35 (2009)
Riesen, K., Bunke, H.: Approximate graph edit distance computation by means of bipartite graph matching. Image Vis. Comput. 27(7), 950–959 (2009)
Riesen, K.: Structural Pattern Recognition with Graph Edit Distance. ACVPR. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-27252-8
Schomburg, I., Chang, A., Ebeling, C., Gremse, M., Heldt, C., Huhn, G., Schomburg, D.: BRENDA, the enzyme database: updates and major new developments. Nucleic Acids Res. 32D, 431–433 (2004)
Shervashidze, N., Vishwanathan, S.V.N., Petri, T., Mehlhorn, K., Borgwardt, K.M.: Efficient graphlet kernels for large graph comparison. In: Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS), pp. 488–495 (2009)
Shervashidze, N., Schweitzer, P., van Leeuwen, E.J., Mehlhorn, K., Borgwardt, K.M.: Weisfeiler-Lehman graph kernels. J. Mach. Learn. Res. (JMLR) 12, 2539–2561 (2011)
Zeng, Z., Tung, A.K.H., Wang, J., Feng, J., Zhou, L.: Comparing stars: on approximating graph edit distance. Proc. Int. Conf. Very Large Database (VLDB) 2(1), 25–36 (2009)
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Kataoka, T., Shiotsuki, E., Inokuchi, A. (2018). Graph Classification with Mapping Distance Graph Kernels. In: De Marsico, M., di Baja, G., Fred, A. (eds) Pattern Recognition Applications and Methods. ICPRAM 2017. Lecture Notes in Computer Science(), vol 10857. Springer, Cham. https://doi.org/10.1007/978-3-319-93647-5_2
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