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Graph Classification Based on Optimizing Graph Spectra

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Discovery Science (DS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6332))

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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

  1. 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)

    Article  MathSciNet  MATH  Google Scholar 

  2. Enron Email Dataset, http://www.cs.cmu.edu/~enron/

  3. 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)

    Article  MathSciNet  MATH  Google Scholar 

  4. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)

    MATH  Google Scholar 

  5. Gärtner, T., Lloyd, J.W., Flach, P.A.: Kernels and Distances for Structured Data. Machine Learning 57(3), 205–232 (2004)

    Article  MATH  Google Scholar 

  6. Hido, S., Kashima, H.: A Linear-Time Graph Kernel. In: Proc. of Int’l Conf. on Data Mining, pp. 179–188 (2009)

    Google Scholar 

  7. Hwang, S.: Cauchy’s Interlace Theorem for Eigenvalues of Hermitian Matrices. American Mathematical Monthly 111, 157–159 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. 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)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kashima, H., Inokuchi, A.: Kernels for graph classification. In: Proc. of ICDM Workshop on Active Mining (2002)

    Google Scholar 

  10. Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized Kernels Between Labeled Graphs. In: Proc. of Int’l Conf. on Machine Learning, pp. 321–328 (2003)

    Google Scholar 

  11. Schölkopf, B., Tsuda, K., Vert, J.: Kernel Methods in Computational Biology. The MIT Press, Cambridge (2004)

    Google Scholar 

  12. Schölkopf, B., Smola, J.: Learning with kernels. MIT Press, Cambridge (2002)

    MATH  Google Scholar 

  13. Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  14. Varma, M., Rakesh Babu, B.: More Generality in Efficient Multiple Kernel Learning. In: Proc. of Int’l Conf. on Machine Learning, vol. 134 (2009)

    Google Scholar 

  15. 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)

    Google Scholar 

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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

  • Print ISBN: 978-3-642-16183-4

  • Online ISBN: 978-3-642-16184-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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