Abstract
In this paper we present a fast subgraph kernel based on Jensen-Shannon divergence and depth-based representations. For graphs with n vertices and m edges, the worst-case time complexity for our kernel is O(n 3 + mn), in contrast to O(n 6) for the classic graph kernel. Key to this efficiency is that we manage to compute the Jensen-Shannon divergence involved in our kernel with O(n 2) operations. This computational strategy enables our subgraph kernel to easily scale up to graphs of reasonably large sizes and thus overcome the size limits arising in state of the art graph kernels. Experiments on standard bioinformatics graph datasets together with graph datasets extracted from images demonstrate the effectiveness and efficiency of our subgraph kernel.
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Amizadeh, S., Wang, S., Hauskrecht, M.: An efficient framework for constructing generalized locally-induced text metrics. In: Proceedings of International Joint Conference on Artificial Intelligence, pp. 1159–1164 (2011)
Bai, L., Hancock, E.: Graph kernels from the Jensen-Shannon divergence. Journal of Mathematical Imaging and Vision (to appear 2013)
Borgwardt, K.M., Kriegel, H.-P.: Shortest-path kernels on graphs. In: Proceedings of the IEEE International Conference on Data Mining, pp. 74–81 (2005)
Crutchfield, J.P., Shalizi, C.R.: Thermodynamic depth of causal states: Objective complexity via minimal representations. Physical Review E 59, 275–283 (1999)
Gärtner, T., Driessens, K., Ramon, J.: Graph kernels and gaussian processes for relational reinforcement learning. In: Proceedings of International Conference on Inductive Logic Programming, pp. 146–163 (2003)
Gärtner, T., Flach, P.A., 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)
Han, L., Escolano, F., Hancock, E.R., Wilson, R.C.: Graph characterizations from von neumann entropy. Pattern Recognition Letters 33, 1958–1967 (2012)
Haussler, D.: Convolution kernels on discrete structures. In: Technical Report UCS-CRL-99-10 (1999)
Johnson, D.B.: Efficient algorithms for shortest paths in sparse networks. Journal of the ACM 24, 1–13 (1977)
Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized kernels between labeled graphs. In: Proceedings of International Conference on Machine Learing, pp. 321–328 (2003)
Martins, A.F., Smith, N.A., Xing, E.P., Aguiar, P.M., Figueiredo, M.A.: Nonextensive information theoretic kernels on measures. Journal of Machine Learning Research 10, 935–975 (2009)
Nori, N., Bollegala, D., Ishizuka, M.: Interest prediction on multinomial, time-evolving social graph. In: Proceedings of International Joint Conference on Artificial Intelligence, pp. 2507–2512 (2011)
Platt, J.C.: Fast training of support vector machines ssing sequential minimal optimization. In: Schölkopf, B., Burges, C.J.C., Smola, A.J. (eds.) Advances in Kernel Methods, pp. 185–208 (1999)
Ren, P., Aleksic, T., Wilson, R.C., Hancock, E.R.: A polynomial characterization of hypergraphs using the ihara zeta function. Pattern Recognition 44, 1941–1957 (2011)
Shervashidze, N., Schweitzer, P., van Leeuwen, E.J., Mehlhorn, K., Borgwardt, K.M.: Weisfeiler-lehman graph kernels. Journal of Machine Learning Research 1, 1–48 (2010)
Shervashidze, N., Vishwanathan, S.V.N., Petri, T., Mehlhorn, K., Borgwardt, K.M.: Efficient graphlet kernels for large graph comparison. Journal of Machine Learning Research 5, 488–495 (2009)
Slater, P.J.: Centers to centroids in graphs. Journal of Graph Theory 2, 209–222 (1978)
Wilson, R.C., Hancock, E.R., Luo, B.: Pattern vectors from algebraic graph theory. IEEE Trans. Pattern Anal. Mach. Intell. 27, 1112–1124 (2005)
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Bai, L., Hancock, E.R. (2013). A Fast Jensen-Shannon Subgraph Kernel. In: Petrosino, A. (eds) Image Analysis and Processing – ICIAP 2013. ICIAP 2013. Lecture Notes in Computer Science, vol 8156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41181-6_19
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DOI: https://doi.org/10.1007/978-3-642-41181-6_19
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