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Kernel Entropy Discriminant Analysis for Dimension Reduction

  • Aditya Mehta
  • C. Chandra Sekhar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10597)

Abstract

The unsupervised techniques for dimension reduction, such as principal component analysis (PCA), kernel PCA and kernel entropy component analysis, do not take the information about class labels into consideration. The reduced dimension representation obtained using the unsupervised techniques may not capture the discrimination information. The supervised techniques, such as multiple discriminant analysis and generalized discriminant analysis, can capture discriminatory information. However the reduced dimension is limited by number of classes. We propose a supervised technique, kernel entropy discriminant analysis (kernel EDA), that uses Euclidean divergence as criterion function. Parzen window method for density estimation is used to find an estimate of Euclidean divergence. Euclidean divergence estimate is expressed in terms of eigenvectors and eigenvalues of the kernel gram matrix. The eigenvalues and eigenvectors that contribute significantly to the Euclidean divergence estimate are used for determining the directions for projection. Effectiveness of the kernel EDA method is demonstrated through the improved classification accuracy for benchmark datasets.

Keywords

Euclidean divergence Parzen windowing 

References

  1. 1.
    Baudat, G., Anouar, F.: Generalized discriminant analysis using a kernel approach. Neural Comput. 12(10), 2385–2404 (2000)CrossRefGoogle Scholar
  2. 2.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley-Interscience, Hoboken (2000)zbMATHGoogle Scholar
  3. 3.
    Fisher, R.A.: The use of multiple measurements in taxonomic problems. Ann. Eugenics 7(2), 179–188 (1936)CrossRefGoogle Scholar
  4. 4.
    Hotelling, H.: Relations between two sets of variates. Biometrika 28(3/4), 321–377 (1936)CrossRefzbMATHGoogle Scholar
  5. 5.
    Izquierdo-Verdiguier, E., Laparra, V., Jenssen, R., Gmez-Chova, L., Camps-Valls, G.: Optimized kernel entropy components. IEEE Trans. Neural Netw. Learn. Syst. 28(6), 1466–1472 (2017)CrossRefGoogle Scholar
  6. 6.
    Jenssen, R.: Kernel entropy component analysis. IEEE Trans. Pattern Anal. Mach. Intell. 32(5), 847–860 (2010)CrossRefGoogle Scholar
  7. 7.
    Mika, S., Ratsch, G., Weston, J., Scholkopf, B., Mullers, K.R.: Fisher discriminant analysis with kernels. In: Proceedings of the 1999 IEEE Signal Processing Society Workshop on Neural Networks for Signal Processing IX, pp. 41–48 (1999)Google Scholar
  8. 8.
    Oliva, A., Torralba, A.: Modeling the shape of the scene: a holistic representation of the spatial envelope. Int. J. Comput. Vision 42(3), 145–175 (2001)CrossRefzbMATHGoogle Scholar
  9. 9.
    Parzen, E.: On estimation of a probability density function and mode. Ann. Math. Stat. 33(3), 1065–1076 (1962)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Principe, J.: Information Theoretic Learning: Renyi’s Entropy and Kernel Perspectives, 1st edn. Springer, New York (2010)CrossRefzbMATHGoogle Scholar
  11. 11.
    Schölkopf, B., Smola, A., Müller, K.-R.: Kernel principal component analysis. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, J.-D. (eds.) ICANN 1997. LNCS, vol. 1327, pp. 583–588. Springer, Heidelberg (1997). doi: 10.1007/BFb0020217 Google Scholar
  12. 12.
    Vogel, J., Schiele, B.: Semantic modeling of natural scenes for content-based image retrieval. Int. J. Comput. Vision 72(2), 133–157 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology MadrasChennaiIndia

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