International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

A Modified Approach to Density-Induced Support Vector Data Description

  • Park, Joo-Young (Department of Control and Instrumentation Engineering, Korea University) ;
  • Kang, Dae-Sung (Department of Control and Instrumentation Engineering, Korea University)
  • Published : 2007.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

The SVDD (support vector data description) is one of the most well-known one-class support vector learning methods, in which one tries the strategy of utilizing balls defined on the feature space in order to distinguish a set of normal data from all other possible abnormal objects. Recently, with the objective of generalizing the SVDD which treats all training data with equal importance, the so-called D-SVDD (density-induced support vector data description) was proposed incorporating the idea that the data in a higher density region are more significant than those in a lower density region. In this paper, we consider the problem of further improving the D-SVDD toward the use of a partial reference set for testing, and propose an LMI (linear matrix inequality)-based optimization approach to solve the improved version of the D-SVDD problems. Our approach utilizes a new class of density-induced distance measures based on the RSDE (reduced set density estimator) along with the LMI-based mathematical formulation in the form of the SDP (semi-definite programming) problems, which can be efficiently solved by interior point methods. The validity of the proposed approach is illustrated via numerical experiments using real data sets.

Keywords

References

  1. Scholkopf, B., Smola, A.J,: Learning with Kernels. MIT Press, Cambridge, MA (2002)
  2. Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge, UK (2004)
  3. Tax, D.M.J., Duin, R.P.W.: Support vector domain description. Pattern Recognition Letters 20 (1999) 1191-1199 https://doi.org/10.1016/S0167-8655(99)00087-2
  4. Tax, D.M.J., Duin, R.P.W.: Support vector data description. Machine Learning 54 (2004) 45-66 https://doi.org/10.1023/B:MACH.0000008084.60811.49
  5. Tax, D.M.J.: One-Class Classification. Ph.D. Thesis, Delft University of Technology (2001)
  6. Lee, K, Kim, D.-W., Lee, D., Lee, K.H.: Improving support vector data description using local density degree. Pattern Recognition 38 (2005) 1768-1771 https://doi.org/10.1016/j.patcog.2005.03.020
  7. Ratsch, G., Mika, S., Scholkopf, B., Muller, K.-R.: Constructing boosting algorithms from SVMs: An application to one-class classification. IEEE Transactions on Pattern Analysis and Machine Intelligence 24 (2002) 1184-1199 https://doi.org/10.1109/TPAMI.2002.1033211
  8. Scholkopf, B., Platt, J. C., Shawe-Taylor, J., Smola, A. J., Williamson, R. C. Estimating the support of a high-dimensional distribution. Neural Computation 13 (2001) 1443-1471 https://doi.org/10.1162/089976601750264965
  9. Lanckriet, G. R. G., El Ghaoui, L., Jordan, M. I.: Robust novelty detection with single-class MPM. Advances in Neural Information Processing Systems 15 (2003) 905-912
  10. Campbell, C., Bennett, K. P.: A linear programming approach to novelty detection. Advances in Neural Information Processing Systems 13 (2001) 395-401
  11. Girolami, M., He, C.: Probabilistic density estimation from optimally condensed data samples. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(2003) 1253-1264 https://doi.org/10.1109/TPAMI.2003.1233899
  12. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia, PA (1994)
  13. Gahinet, P., Nemirovski, A., Laub, A.J., ChilaH, M.: LMI Control Toolbox. MathWorks Inc., Natick, MA (1995)
  14. Lee, K, Lee, D., Lee, K.H.: A new data description method based on the density-induced support vector information. In: Proceedings of the 6th International Symposium on Advanced Intelligent Systems (2005) 616-621
  15. Blake, C. L., Merz, C. J., UCI Repos-itory of Machine Learning Database, www.ics.uci.edu/-mlearn/MLRepository.html, 1998

Cited by

  1. Some Observations for Portfolio Management Applications of Modern Machine Learning Methods vol.16, pp.1, 2016, https://doi.org/10.5391/IJFIS.2016.16.1.44