The Marketing Book 5th Edition

Inputs

Kohonen

nodes

Quantitative methods in marketing 221

solving problems in retailing institutions,
where the model helps management to decide
on the size of their salesforce. Perhaps it was
the successful application of this technique in
this area of marketing that has contributed to
its vast improvements and wide applications.
There are, however, limitations to this tech-
nique, one of which is that queuing systems
must be operated over a sufficiently long
period to achieve a steady-state solution, and it
is often difficult to predict the length of time
required to achieve this.

Self-organizing maps (SOMs)

The Kohonen self-organizing map

Following Gurney (1997), for example, we
define a neural network (NN) as a collection of
interrelated nodes. Definitions of this nature
remove the need to rely on analogies of the
brain and take us into more general domains, in
which the nodes amount to what are known
more familiarly as variables. Neural network
techniques have become an accepted part of the
‘toolkit’ available to researchers in numerous
fields. There are other less well-known NN
techniques which also hold much potential,
and perhaps the most notable of these is the
Kohonen SOM. Neelakanta (1999) described
self-organization as the ‘progressive formation
within the system of sequential, ordered rela-
tionships between the interacting dynamic
variables’. One might also describe the phe-
nomenon as ‘adaptation’. The SOM provides,
quite literally, a picture or map of a set of data,
but it does so in an adaptive or ‘intelligent’ way.
On the other hand, NNs in general, including
those which apply supervised learning, are also
self-organizing in a similar sense: e.g. the
hidden nodes in perceptron models provide
approximations to an underlying function and
can act to filter the data.
The SOM amounts to a relationship
between a set of input nodes and a set of nodes
connected to these inputs which perform the
operations of transformation and grouping.

There is no output node serving the role of

predicted or target value and hence in NN

terminology we have ‘unsupervised learning’.

Specifically, these ‘Kohonen’ nodes are

arranged in a two-dimensional grid, with each

node being connected to each of the inputs, as

shown in Figure 9.7.

Interestingly, the actual spacing of the

Kohonen nodes has no meaning: what is

important is their grouping together. This is

because each node is regarded as a ‘prototype’,

a set of cognate values of the attributes of the

input data. An equivalent term is ‘reference

vector’. These values are the weights of the

node. As discussed below, each vector of

observed values, which may be continuous,

discrete or categorical, will be closest in terms

of Euclidean distance to one particular proto-

type node. The latter nodes serve to classify or

cluster inputs, but the proximity of each node

to its neighbours in the grid is a key element,

which distinguishes the SOM from conven-

tional statistical clustering techniques. Whereas

cluster analysis (CA) operates in the space of

actual data values, the SOM operates within its

own two-dimensional grid. Standard methods

of CA are almost invariably designed to pro-

duce non-overlapping clusters (Everitt, 1993),

but the prototypes of the SOM are not mutually

exclusive. This means that the final feature

map, instead of showing several distinct

clusters with differing characteristics, shows

neighbouring nodes which have many similar

Figure 9.7 A self-organizing map. Connections

operate between all inputs and all Kohonen nodes