Self-Organizing Maps and Unsupervised Classification - Neural Networks: Methodology and Applications - page 421

n c p ( z )

z )=
c∈C i

c∈C i

p ( l i | p ( c | z )=

n r p r ( z )

r∈C

where

p c ( z )= 1
T c

K T ( δ ( c,r )) f r ( z , w ,σ r ) .

c

Note that this probability relies on the labeling of the map. That step is
crucial for the computation of the posterior probabilities. Their consistency
depends on the quality of the map. Thus, the classifier performances depend
jointly on the amount of expert data, on the accuracy of the approximation
of the observation density, and on the topological order that is built by the
self-organization process.
The knowledge of posterior probabilities leads to a classification rule that
is based on probabilistic estimation. Using those relations, the vector of class
membership probabilities can be computed for each observation z . Finally,
the assignment of the observation to a class is performed by the application of
Bayes rule: choose the class for which the membership probability is highest.

7.5 Applications

Self-organizing maps gave rise to a large number of applications. Specific de-
velopments were required for some of them, but they are in actual operation.
At the moment, the most important research center for those topics is lo-
cated at University of Technology of Helsinki (UTH). The major part of the
research that is developed in its computer science laboratory (Laboratory of
Computer and Information Science) is performed by the Neural Network Re-
search Center, created by T. Kohonen in 1994, and now headed by E. Oja.
The description of a large number of applications is now available on the Web
site of NNR (http://www.cis.hut.fi/research/). The main research axis and the
current applications are generally focused on self-organizing maps. Companies
now exploit many applications. They arose from original, multidisciplinary re-
search, and several research groups specialized such fields as bioinformatics,
speech and writing analysis and recognition, and image analysis.
Actually, the implementation of self-organizing maps into larger systems
widely uses the specific features of the application domain. The coding of the
information, the organization of data bases, the analysis and visualization of
the data, require specific, multidisciplinary research whose results are crucial
for the performance of the self-organizing maps.
In the following, two applications will be described in detail. They were
selected as representative of the domains to which self-organizing maps are
relevant. The target of this presentation is twofold: