Supervised Transform Learning for Face Recognition

  • Dimche Kostadinov
  • Sviatoslav Voloshynovskiy
  • Sohrab Ferdowsi
  • Maurits Diephuis
  • Rafał Scherer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9119)

Abstract

In this paper we investigate transform learning and apply it to face recognition problem. The focus is to find a transformation matrix that transforms the signal into a robust to noise, discriminative and compact representation. We propose a method that finds an optimal transform under the above constrains. The non-sparse variant of the presented method has a closed form solution whereas the sparse one may be formulated as a solution to a sparsity regularized problem. In addition we give a generalized version of the proposed problem and we propose a prior on the data distribution across the dimensions in the transform domain.

Supervised transform learning is applied to the MVQ [10] method and is tested on a face recognition application using the YALE B database. The recognition rate and the robustness to noise is superior compared to the original MVQ based on k-means.

Keywords

Supervised sparsifying transform Sparse representation Dictionary learning Face recognition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahmed, N., Natarajan, T., Rao, K.R.: Discrete cosine transfom. IEEE Trans. Comput. 23(1), 90–93 (1974)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Beaton, A.E., Tukey, J.W.: The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data. Technometrics 16(2), 147–185 (1974)CrossRefGoogle Scholar
  3. 3.
    Bell, A.J., Sejnowski, T.J.: The “independent components” of natural scenes are edge filters. Vision Research 37, 3327–3338 (1997)CrossRefMATHGoogle Scholar
  4. 4.
    Child, D.: The Essentials of Factor Analysis. Bloomsbury Academic (2006)Google Scholar
  5. 5.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing). Wiley-Interscience (2006)Google Scholar
  6. 6.
    Fisher, R.A.: The use of multiple measurements in taxonomic problems. Annals of Eugenics 7(2), 179–188 (1936)CrossRefGoogle Scholar
  7. 7.
    Georghiades, A.S., Belhumeur, P.N., Kriegman, D.J.: From few to many: Illumination cone models for face recognition under variable lighting and pose. IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 643–660 (2001)CrossRefGoogle Scholar
  8. 8.
    Huber, P.J.: Robust estimation of a location parameter. Annals of Mathematical Statistics 35(1), 73–101 (1964)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Jolliffe, I.: Principal Component Analysis. Springer Series in Statistics. Springer (2002)Google Scholar
  10. 10.
    Kostadinov, D., Voloshynovskiy, S., Diephuis, M.: Visual information encoding for face recognition: sparse coding vs vector quantization. In: 4th Joint WIC IEEE Symposium on Information Theory and Signal Processing in the Benelux, Eindhoven, Netherlands, vol. 35 (May 2014)Google Scholar
  11. 11.
    Lay, D.C.: Linear Algebra and Its Applications, 4th edn. Addison-Wesley (2006)Google Scholar
  12. 12.
    Elad, M., Milanfar, P., Rubinstein, R.: Analysis versus synthesis in signal priors. Inverse Problems 23(3), 947–968 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Martinez, A.M., Kak, A.C.: Pca versus lda. IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 228–233 (2001)CrossRefGoogle Scholar
  14. 14.
    Rubinstein, R., Peleg, T., Elad, M.: Analysis k-svd: A dictionary-learning algorithm for the analysis sparse model. IEEE Transactions on Signal Processing 61(3), 661–677 (2013)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Ravishankar, S., Bresler, Y.: ℓ0 sparsifying transform learning with efficient optimal updates and convergence guarantees. CoRR abs/1501.02859 (2015)Google Scholar
  16. 16.
    Bracewell, R.N.: The Fourier Transform and Its Applications. Electrical engineering series. McGraw Hill (2000)Google Scholar
  17. 17.
    Stphane, M.: A Wavelet Tour of Signal Processing: The Sparse Way, 3rd edn. Academic Press (2008)Google Scholar
  18. 18.
    Zdunek, R., Cichocki, A.: Non-negative matrix factorization with quasi-newton optimization. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 870–879. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Dimche Kostadinov
    • 1
  • Sviatoslav Voloshynovskiy
    • 1
  • Sohrab Ferdowsi
    • 1
  • Maurits Diephuis
    • 1
  • Rafał Scherer
    • 2
  1. 1.Computer Science DepartmentUniversity of GenevaGenevaSwitzerland
  2. 2.Institute of Computational IntelligenceCzȩstochowa University of TechnologyCzȩstochowaPoland

Personalised recommendations