Self-Organizing Maps and Unsupervised Classification - Neural Networks: Methodology and Applications - page 401

Fig. 7.11. Representation of the order that is induced by the topological map. The
maps are obtained for different cooling schedules of T , the same random initialization
at the center of the observation cloud and the same variation interval for T

general rule guarantees an appropriate self-organization of the reference vector
set. Therefore, it is advisable to test that the algorithm has performed well and
that the final set of reference vectors exhibits appropriate self-organization. A
relevant real-life example is described in detail below.
For implementation purpose, the batch algorithm of topological maps for
a usual cooling schedule can be summarized as follows:

Batch Optimization of Topological Maps (T Decreasing)

1. Initialization: perform the dynamic clustering SOM (Self-organizing map)
algorithm for T = T max , set t =0
2. Iteration t. The reference vector set W t− 1 is known from previous step.
Compute the new temperature value according to the cooling schedule:
T = T max T min
T max

t
N iter − 1

For that temperature T , perform sequentially the two following phases:
• Allocation: update the allocation function that is associated to W t− 1 .

A reference vector is allocated to each observation belonging to the
training data from relation:

χ T ( z ) = arg max
r∈C

2 =argmax
r∈C

d T ( z , w r ) . K T ( δ ( c,r )) z − w c

c∈C

• Minimization: apply relation