A Fixed-Point Algorithm of Topographic ICA

  • Yoshitatsu Matsuda
  • Kazunori Yamaguchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4132)


Topographic ICA is a well-known ICA-based technique, which generates a topographic mapping consisting of edge detectors from natural scenes. Topographic ICA uses a complicated criterion derived from a two-layer generative model and minimizes it by a gradient descent algorithm. In this paper, we propose a new simple criterion for topographic ICA and construct a fixed-point algorithm minimizing it. Our algorithm can be regarded as an expansion of the well-known fast ICA algorithm to topographic ICA, and it does not need any tuning of the stepsize. Numerical experiments show that our fixed-point algorithm can generate topographic mappings similar to those in topographic ICA.


Independent Component Analysis Independent Component Analysis Natural Scene Blind Signal Neighborhood Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Jutten, C., Herault, J.: Blind separation of sources (part I): An adaptive algorithm based on neuromimetic architecture. Signal Processing 24, 1–10 (1991)MATHCrossRefGoogle Scholar
  2. 2.
    Comon, P.: Independent component analysis - a new concept? Signal Processing 36, 287–314 (1994)MATHCrossRefGoogle Scholar
  3. 3.
    Bell, A.J., Sejnowski, T.J.: An information-maximization approach to blind separation and blind deconvolution. Neural Computation 7, 1129–1159 (1995)CrossRefGoogle Scholar
  4. 4.
    Cardoso, J.F., Laheld, B.: Equivariant adaptive source separation. IEEE Transactions on Signal Processing 44, 3017–3030 (1996)CrossRefGoogle Scholar
  5. 5.
    Hyvärinen, A., Hoyer, P.O., Inki, M.: Topographic independent component analysis. Neural Computation 13, 1527–1558 (2001)MATHCrossRefGoogle Scholar
  6. 6.
    Hyvärinen, A., Hoyer, P.O.: A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images. Vision Research 41, 2413–2423 (2001)CrossRefGoogle Scholar
  7. 7.
    Matsuda, Y., Yamaguchi, K.: The InfoMin principle: a unifying information-based criterion for forming topographic mappings. In: ICONIP 2001 Proceedings, Shanghai, China, pp. 14–19 (2001)Google Scholar
  8. 8.
    Matsuda, Y., Yamaguchi, K.: The InfoMin criterion: an information theoretic unifying objective function for topographic mappings. In: Kaynak, O., Alpaydın, E., Oja, E., Xu, L. (eds.) ICANN 2003 and ICONIP 2003. LNCS, vol. 2714, pp. 401–408. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Matsuda, Y., Yamaguchi, K.: The infomin principle for ica and topographic mappings. In: Rosca, J.P., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 958–965. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Hyvärinen, A., Oja, E.: A fast fixed-point algorithm for independent component analysis. Neural Computation 9, 1483–1492 (1997)CrossRefGoogle Scholar
  11. 11.
    Hyvärinen, A.: Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks 10, 626–634 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yoshitatsu Matsuda
    • 1
  • Kazunori Yamaguchi
    • 2
  1. 1.Department of Integrated Information TechnologyAoyama Gakuin UniversityKanagawaJapan
  2. 2.Department of General Systems StudiesThe University of TokyoTokyoJapan

Personalised recommendations