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- T. Graepel, M. Burger, and
K. Obermayer. Self-Organizing Maps: generalizations and New Optimization
Techniques.
.
Neurocomputing, 20:173-190, 1998.
(FTP Gzipped PostScript, 21 pages, 116 kb)
We offer three algorithms for the generation of topographic
mappings to the practitioner of unsupervised data analysis. The algorithms
are each based on the minimization of a cost function which is performed
using an EM algorithm and deterministic annealing. The soft topographic
vector quantization algorithm (STVQ) -- like the original Self-Organizing Map
(SOM) -- provides a tool for the creation of self-organizing maps of
Euclidean data. Its optimization scheme, however, offers an alternative to
the heuristic stepwise shrinking of the neighborhood width in the SOM and
makes it possible to use a fixed neighborhood function solely to encode
desired neighborhood relations between nodes. The kernel-based soft
topographic mapping (STMK) is a generalization of STVQ and introduces new
distance measures in data space based on kernel functions. Using the new
distance measures corresponds to performing the STVQ in a high-dimensional
feature space, which is related to data space by a nonlinear mapping. This
preprocessing can reveal structure of the data which may go unnoticed if the
STVQ is performed in the standard Euclidean space. The soft topographic
mapping for proximity data (STMP) is another generalization of STVQ that
enables the user to generate topographic maps for data which are given in
terms of pairwise proximities. It thus offers a flexible alternative to
multidimensional scaling methods and opens up a new range of applications for
Self-Organizing Maps. Both STMK and STMP share the robust optimization
properties of STVQ due to the application of deterministic annealing. In our
contribution we discuss the algorithms together with their implementation and
provide detailed pseudo-code and explanations.
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