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Similarity and Kernel Matrix Evaluation Based on Spatial Autocorrelation Analysis

  • Vincent Pisetta
  • Djamel A. Zighed
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5722)

Abstract

We extend the framework of spatial autocorrelation analysis on Reproducing Kernel Hilbert Space (RKHS). Our results are based on the fact that some geometrical neighborhood structures vary when samples are mapped into a RKHS, while other neighborhood structures do not. These results allow us to design a new measure for measuring the goodness of a kernel and more generally a similarity matrix. Experiments on UCI datasets show the relevance of our methodology.

Keywords

Kernel matrix evaluation spatial autocorrelation similarity learning 

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References

  1. 1.
    Vapnik, N.V.: The Nature of Statistical Learning Theory. Springer, New York (2000)CrossRefzbMATHGoogle Scholar
  2. 2.
    Schölkopf, B., Smola, A.J.: Learning with kernels. MIT Press, Cambridge (2002)zbMATHGoogle Scholar
  3. 3.
    Fine, S., Scheinberg, K.: Efficient SVM training using low-rank kernel representations. Journal of Machine Learning Research, Res. 2, 243–264 (2002)zbMATHGoogle Scholar
  4. 4.
    Ong, C.S., Smola, A.J., Williamson, R.C.: Learning the kernel with hyperkernels. Journal of Machine Learning Research. Res. 6, 1043–1071 (2005)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Cristianini, N., Shawe-Taylor, J., Elisseeff, A., Kandola, J.: On kernel-target alignment. In: Dietterich, T.G., Becker, S., Ghahramani, Z. (eds.) Advances in Neural Information Processing Systems. MIT Press, Cambridge (2001)Google Scholar
  6. 6.
    Nguyen, C., Ho, T.B.: An efficient kernel matrix evaluation measure. Pattern Recognition 41(11), 3366–3372 (2008)CrossRefzbMATHGoogle Scholar
  7. 7.
    Zighed, D.A., Lallich, S., Muhlenbach, F.: Separability Index in Supervised Learning. In: Elomaa, T., Mannila, H., Toivonen, H. (eds.) PKDD 2002. LNCS (LNAI), vol. 2431, pp. 475–487. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Rao, C.: Linear statistical inference and its applications. Wiley, New York (1965)zbMATHGoogle Scholar
  9. 9.
    Toussaint, G.: The relative neighborhood graph of finite planar set. Pattern recognition 12, 261–268 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Shin, H., Cho, S.: Invariance of neighborhood relation under input space to feature space mapping. Pattern Recognition Letters 26, 707–718 (2005)CrossRefGoogle Scholar
  11. 11.
    Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geomatric framework for nonlinear dimensionality reduction. In: Advances in Neural Information Processing Systems, vol. 10, pp. 682–687. MIT Press, Cambridge (2000)Google Scholar
  12. 12.
    Kruskal, J.B., Wish, M.: Multidimensional Scaling. Sage Univerity Paper series on Quantitative Application in the Social Sciences, 07-011. Sage Publications, Beverly Hills (1978)CrossRefGoogle Scholar
  13. 13.
    Chang, C.C., Lin, C.J.: LIBSVM: a library for support vector machines (2001)Google Scholar
  14. 14.
    Hacid, H., Zighed, D.A.: An Effective Method for Locally Neighborhood Graphs Updating. Database and Expert Systems Applications. In: 16th International Conference, DEXA, Copenhagen, Denmark (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Vincent Pisetta
    • 1
  • Djamel A. Zighed
    • 2
  1. 1.RithmeLyonFrance
  2. 2.ERIC LaboratoryBronFrance

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