Abstract
Kernel methods such as the SVM are becoming increasingly popular due to their high performance in graph classification. In this paper, we propose a novel graph kernel, called SPEC, based on graph spectra and the Interlace Theorem, as well as an algorithm, called OPTSPEC, to optimize the SPEC kernel used in an SVM for graph classification. The fundamental performance of the method is evaluated using artificial datasets, and its practicality confirmed through experiments using a real-world dataset.
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References
Alon, N., Krivelevich, M., Vu, V.H.: On the Concentration of Eigenvalues of Random Symmetric Matrices. Israel Journal of Mathematics 131(1), 259–267 (2001)
Enron Email Dataset, http://www.cs.cmu.edu/~enron/
Freund, Y., Schapire, R.E.: A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting. Journal of Computer and System Sciences 55(1), 119–139 (1997)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)
Gärtner, T., Lloyd, J.W., Flach, P.A.: Kernels and Distances for Structured Data. Machine Learning 57(3), 205–232 (2004)
Hido, S., Kashima, H.: A Linear-Time Graph Kernel. In: Proc. of Int’l Conf. on Data Mining, pp. 179–188 (2009)
Hwang, S.: Cauchy’s Interlace Theorem for Eigenvalues of Hermitian Matrices. American Mathematical Monthly 111, 157–159 (2004)
Ikebe, Y., Inagaki, T., Miyamoto, S.: The monotonicity theorem, Cauchy’s interlace theorem, and the Courant-Fischer theorem. American Mathematical Monthly 94, 352–354 (1987)
Kashima, H., Inokuchi, A.: Kernels for graph classification. In: Proc. of ICDM Workshop on Active Mining (2002)
Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized Kernels Between Labeled Graphs. In: Proc. of Int’l Conf. on Machine Learning, pp. 321–328 (2003)
Schölkopf, B., Tsuda, K., Vert, J.: Kernel Methods in Computational Biology. The MIT Press, Cambridge (2004)
Schölkopf, B., Smola, J.: Learning with kernels. MIT Press, Cambridge (2002)
Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)
Varma, M., Rakesh Babu, B.: More Generality in Efficient Multiple Kernel Learning. In: Proc. of Int’l Conf. on Machine Learning, vol. 134 (2009)
Vishwanathan, S.V.N., Borgwardt, K.M., Schraudolph, N.N.: Fast Computation of Graph Kernels. In: Proc. of Annual Conf. on Neural Information Processing Systems, pp. 1449–1456 (2006)
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Vinh, N.D., Inokuchi, A., Washio, T. (2010). Graph Classification Based on Optimizing Graph Spectra. In: Pfahringer, B., Holmes, G., Hoffmann, A. (eds) Discovery Science. DS 2010. Lecture Notes in Computer Science(), vol 6332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16184-1_15
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DOI: https://doi.org/10.1007/978-3-642-16184-1_15
Publisher Name: Springer, Berlin, Heidelberg
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