Solving the One-Class Problem Using Neighbourhood Measures

  • Javier M. Moguerza
  • Alberto Muñoz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3138)

Abstract

The problem of estimating high density regions from univariate or multivariate data samples is studied. To be more precise, we estimate minimum volume sets, whose probability is specified in advance. This problem arises in outlier detection and cluster analysis, and is strongly related to One-Class Support Vector Machines (SVM). In this paper we propose a new method to solve this problem, the Support Neighbour Machine (SNM). We show its properties and introduce a new class of kernels. Finally, numerical results illustrating the advantage of the new method are shown.

Keywords

Support Vector Machine Outlier Detection Support Vector Machine Algorithm High Density Region True Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Devroye, L.: Recursive estimation of the mode of a multivariate density. The Canadian Journal of Statistics 7(2), 159–167 (1979)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Mangasarian, O.L., Wolberg, W.H.: Cancer diagnosis via linear programming. SIAM News 23(5), 1–18 (1990)Google Scholar
  3. 3.
    Moguerza, J.M., Muñoz, A., Martin-Merino, M.: Detecting the Number of Clusters Using a Support Vector Machine Approach. In: Dorronsoro, J.R. (ed.) ICANN 2002. LNCS, vol. 2415, pp. 763–768. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Muñoz, A., Muruzabal, J.: Self-Organizing Maps for Outlier Detection. Neurocomputing 18, 33–60 (1998)CrossRefGoogle Scholar
  5. 5.
    Rätsch, G., Mika, S., Schölkopf, B., Müller, K.R.: Constructing Boosting Algorithms from SVMs: an Application to One-Class Classification. IEEE Trans. on Pattern Analysis and Machine Intelligence 24(9), 1184–1199 (2002)CrossRefGoogle Scholar
  6. 6.
    Schölkopf, B., Burges, C., Vapnik, V.: Extracting Support Data for a given Task. In: Proc. of the First International Conference on Knowledge Discovery and Data Mining, AAAI Press, Menlo Park (1995)Google Scholar
  7. 7.
    Schölkopf, B., Platt, J.C., Shawe-Taylor, J., Smola, A.J., Williamson, R.C.: Estimating the Support of a High Dimensional Distribution. Neural Computation 13(7), 1443–1471 (2001)MATHCrossRefGoogle Scholar
  8. 8.
    Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, Boca Raton (1990)Google Scholar
  9. 9.
    Tax, D.M.J., Duin, R.P.W.: Support Vector Domain Description. Pattern Recognition Letters 20, 1991–1999 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Javier M. Moguerza
    • 1
  • Alberto Muñoz
    • 2
  1. 1.University Rey Juan CarlosMóstolesSpain
  2. 2.University Carlos IIIGetafeSpain

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