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Kernel-Based Topographic Maps: Theory and Applications

  1. Marc M. Van Hulle

Published Online: 16 MAR 2009

DOI: 10.1002/9780470050118.ecse365

Wiley Encyclopedia of Computer Science and Engineering

Wiley Encyclopedia of Computer Science and Engineering

How to Cite

Van Hulle, M. M. 2009. Kernel-Based Topographic Maps: Theory and Applications. Wiley Encyclopedia of Computer Science and Engineering. 1633–1650.

Author Information

  1. K.U. Leuven, Campus Gasthuisberg, Leuven, Belgium

Publication History

  1. Published Online: 16 MAR 2009

Abstract

The self-organizing map (SOM) algorithm, originally introduced by Teuvo Kohonen, has seen an incredible range of applications, especially because of its unique abilities to cluster and visualize high-dimensional data. The data are projected onto a topographic map, a discrete lattice that locally approximates the data manifold. Several adaptations to the original concept have been introduced, but one that uses kernels to represent the local density of the manifold has received much attention. In this way, one expects that clusters in the data can be better visualized in the topographic map. For these kernel-based topographic maps, kernel topographic maps, or probabilistic topographic maps, several learning principles have been proposed, mostly for Gaussian kernels. We review these learning algorithms, distinguish between homoscedastic and heteroscedastic Gaussian kernels with a focus on fixed point rules, and show some successful applications.

Keywords:

  • topographic maps;
  • self organization;
  • SOM algorithm;
  • kernel;
  • fixed point;
  • discrete lattice;
  • data manifold;
  • data visualization;
  • density estimation;
  • clustering