Self-Organizing Maps and Unsupervised Classification - Neural Networks: Methodology and Applications - page 381

algorithms of pattern recognition and clustering. The formalism that we use
here is slightly different from the original Kohonen formalism. We will discuss
all the necessary links between the various versions of the basic algorithm.
Then a section will show in detail how expert knowledge can be used after
performing unsupervised training.
This chapter is also application-oriented to a large extent. Two detailed
studies of real-world applications are presented. Numerous self-organizing map
based concrete projects were carried out in various application fields. Some re-
cent topics describe some of those applications [Oja et al. 1999; Kohonen 2001].
A review paper provides a fairly complete bibliography of all papers published
between 1981 and 1997 ([Kaski et al. 1998] www.soe.ucsc.edu/NCS). The
Helsinki University Web site (http://www.cis.hut.fi/ research/som-research/)
addresses a large variety of topics: computer vision, image analysis, image
compression, medical imagery, handwriting recognition, speech recognition,
signal analysis, music analysis, process control, robotics, Web searching and
so on.
The first application that is described in the present chapter deals with re-
mote sensing. By analyzing the details of the modeling that was performed, we
will help understand how self-organizing maps are used to perform data analy-
sis. Kohonen's research group performed the second application: the Websom
system, which is aimed at document searching on the Web. This application
is interesting because the relevant data exhibit very large dimensionality. It
is a striking example demonstrating the expected computational power of
self-organizing maps.

7.1 Notations and Definitions

This section defines the notations that will be used throughout the present
chapter. The set D denotes the observation space. We assume that the obser-
vations are real-valued and multidimensional; therefore, D is a subset of the
n -dimensional vector space R n . Each vector belonging to D is associated to

a particular encoding of an individual observation, which is taken from the
given population. N observation vectors are assumed to be available: they are
associated to N individuals. They form the subset A =

.Ac-
tually, A is included in D . Naturally, it is assumed that A is a representative
sample of the considered population. According to that assumption, A is the
training set that allows parametric estimation.
All the methods that will be described aim, in a first step, at reducing the
information that is present in D .Theydoso

{ z i ; i =1 ,...,N }

• by building a finite subset W = of D ;those n -

dimensional vectors will be called reference vectors or simply reference
throughout this chapter;

{ w c ; c =1 ,...,p }