Advertisement

Self-organization of Probabilistic PCA Models

  • Ezequiel López-Rubio
  • Juan Miguel Ortiz-de-Lazcano-Lobato
  • Domingo López-Rodríguez
  • María del Carmen Vargas-González
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4507)

Abstract

We present a new neural model, which extends Kohonen’s self-organizing map (SOM) by performing a Probabilistic Principal Components Analysis (PPCA) at each neuron. Several self-organizing maps have been proposed in the literature to capture the local principal subspaces, but our approach offers a probabilistic model at each neuron while it has linear complexity on the dimensionality of the input space. This allows to process very high dimensional data to obtain reliable estimations of the local probability densities which are based on the PPCA framework. Experimental results are presented, which show the map formation capabilities of the proposal with high dimensional data.

Keywords

Probabilistic Principal Components Analysis (PPCA) competitive learning unsupervised learning dimensionality reduction face recognition handwritten digit recognition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Daniel, G., Chen, M.: Video Visualization Benchmark Resources (November 2006), http://www.swan.ac.uk/compsci/research/graphics/vg/video/
  2. 2.
    Kohonen, T.: The Self-Organizing Map. Proc. IEEE 78, 1464–1480 (1990)CrossRefGoogle Scholar
  3. 3.
    LeCun, Y., Cortes, C.: The MNIST Database of Handwritten Digits (November 2006), http://yann.lecun.com/exdb/mnist/
  4. 4.
    Tenenbaum, J.B., de Silva, V., Langford, J.C.: Data sets for nonlinear dimensionality reduction (November 2006), http://isomap.stanford.edu/datasets.html
  5. 5.
    Tipping, M.E., Bishop, C.M.: A Hierarchical Latent Variable Model for Data Visualization. IEEE Trans. on Pattern Analysis and Machine Intelligence 20(3), 281–293 (1998)CrossRefGoogle Scholar
  6. 6.
    Tipping, M.E., Bishop, C.M.: Mixtures of Probabilistic Principal Components nalyzers. Neural Computation 11, 443–482 (1999)CrossRefGoogle Scholar
  7. 7.
    Van Hulle, M.M.: Joint Entropy Maximization in Kernel-Based Topographic Maps. Neural Computation 14(8), 1887–1906 (2002)zbMATHCrossRefGoogle Scholar
  8. 8.
    Verbeek, J.J., Vlassis, N., Krose, B.J.A.: Self-organizing mixture models. Neurocomputing 63, 99–123 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ezequiel López-Rubio
    • 1
  • Juan Miguel Ortiz-de-Lazcano-Lobato
    • 1
  • Domingo López-Rodríguez
    • 1
  • María del Carmen Vargas-González
    • 1
  1. 1.School of Computer Engineering, University of Málaga, Campus de Teatinos, s/n. 29071 MálagaSpain

Personalised recommendations