Quantitative methods in marketing 223
(1992), who make an analogy with data com-
pression techniques, in which the primary aim is
subsequent reconstruction of the data with
minimal error. They show that the SOM has a
similar interpretation, whereby the learning
procedure amounts to a search for a set of
weights to minimize the expected reconstruc-
tion error. The learning rule embodies the
principle of gradient descent and there is
therefore an element of similarity with back-
propagation. Also, as well as being an independ-
ent statistical procedure in its own right, the
SOM may be used as a pre-filter to other forms of
NN, for instance to a standard multiplayer
perceptron using back-propagation.
Business applications
SOMs have been shown to be useful in different
types of business applications. Mazanec (1995)
analysed positioning issues related to luxury
hotels, using SOMs based on the discrete-value
neighbourhood technique. Using data on per-
ceptions of hotels and customer satisfaction, he
showed that the non-parametric nature of this
analysis allowed for compression of binary
profile data.
Cottrell et al. (1998) applied the SOM in a
forecasting context, with the nodes in the
Kohonen layer used to store profiles describing
the shapes of various trends, as opposed to
relying solely on traditional parameters such as
mean and standard deviation.
Serrano Cimca (1998) examined strategic
groupings among Spanish savings banks, using
a combination of SOMs and CA. The idea of the
strategic group is often used to explain relation-
ships between firms in the same sector, but here
the groups were identified using only data
from published financial information, thus giv-
ing groups of firms that followed similar
financial strategies, with similar levels of profit-
ability, cost structures, etc. The methodology
allowed the visualization of similarities
between firms in an intuitive manner, and
showed up profound regional differences
between Spanish savings banks.
The Kohonen SOM is a form of NN, which
shares with other networks an origin in models
of neural processing. As with other NNs,
applications of such methods tend to take us
into the realm of statistics, with the SOM
operating as a new and interesting variant on
CA. The aim is to provide a ‘topology preserv-
ing’ data transformation onto a two-dimen-
sional grid, in which the location of the nodes
vis-`a-viseach other is important.
The SOM has some similarities with CA, in
the sense that both involve ‘unsupervised
learning’, where there is no dependent variable.
Most clustering techniques involve attempts to
find non-overlapping groups, so that each data
point belongs uniquely. In the SOM, however,
each data point is associated with the nearest
prototype, but this does not exclude an associa-
tion with others. Indeed, the fact that Kohonen
nodes are spatially related in defined ‘neigh-
bourhoods’ is an important feature of the
approach. Clustering and SOMs tend to show
us different aspects of the data. Clustering, by
its concentration on differences, points out the
observations that do not conform, while SOMs
concentrate on similarities and gradual changes
in the data. The relationships between proto-
types are a key part of the model. One may
navigate between them, and important attri-
butes of the data set may be found in groups of
prototypes.
It is also possible to employ the SOM in a
predictive format, involving supervised learn-
ing. It can be used in this way as a pre-filter to
a predictive NN using methods such as back-
propagation. The model first of all derives a
Kohonen map, and then applies supervised
learning as a second step.Stochastic processes
A stochastic process is a random experiment
which occurs over time, the outcome of which
is determined by chance. From these random
experiments some attributes of interest are
observed and numerical values can be given to
these attributes according to the probability