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Kernel Entropy Component Analysis Pre-images for Pattern Denoising

  • Robert Jenssen
  • Ola Storås
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5575)

Abstract

The recently proposed kernel entropy component analysis (kernel ECA) technique may produce strikingly different spectral data sets than kernel PCA for a wide range of kernel sizes. In this paper, we investigate the use of kernel ECA as a component in a denoising technique previously developed for kernel PCA. The method is based on mapping noisy data to a kernel feature space, for then to denoise by projecting onto a kernel ECA subspace. The denoised data in the input space is obtained by computing pre-images of kernel ECA denoised patterns. The denoising results are in several cases improved.

Keywords

Input Space Kernel Matrix Neural Information Processing System Kernel Size Kernel Principal Component Analysis 
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.
    Jenssen, R., Eltoft, T., Girolami, M., Erdogmus, D.: Kernel Maximum Entropy Data Transformation and an Enhanced Spectral Clustering Algorithm. In: Advances in Neural Information Processing Systems 19, pp. 633–640. MIT Press, Cambridge (2007)Google Scholar
  2. 2.
    Schölkopf, B., Smola, A.J., Müller, K.-R.: Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation 10, 1299–1319 (1998)CrossRefGoogle Scholar
  3. 3.
    Mika, S., Schölkopf, B., Smola, A., Müller, K.R., Scholz, M., Rätsch, G.: Kernel PCA and Denoising in Feature Space. In: Advances in Neural Information Processing Systems, 11, pp. 536–542. MIT Press, Cambridge (1999)Google Scholar
  4. 4.
    Kwok, J.T., Tsang, I.W.: The Pre-Image Problem in Kernel Methods. IEEE Transactions on Neural Networks 15(6), 1517–1525 (2004)CrossRefGoogle Scholar
  5. 5.
    Park, J., Kim, J., Kwok, J.T., Tsang, I.W.: SVDD-Based Pattern Denoising. Neural Computation 19, 1919–1938 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Jenssen, R., Erdogmus, D., Principe, J.C., Eltoft, T.: The Laplacian PDF Distance: A Cost Function for Clustering in a Kernel Feature Space. In: Advances in Neural Information Processing Systems 17, pp. 625–632. MIT Press, Cambridge (2005)Google Scholar
  7. 7.
    Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  8. 8.
    Murphy, R., Ada, D.: UCI Repository of Machine Learning databases. Tech. Rep., Dept. Comput. Sci. Univ. California, Irvine (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Robert Jenssen
    • 1
  • Ola Storås
    • 1
  1. 1.Department of Physics and TechnologyUniversity of TromsøTromsøNorway

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