Self-Organizing Maps and Unsupervised Classification - Neural Networks: Methodology and Applications - page 399

Fig. 7.9. Observation set and initial order generated on the map by random selection
of the reference vectors

cloud according to a peaked Gaussian law (its standard deviation is equal to
0.01). Initially, no ordering between the positions of the reference vectors can
be observed.
Figure 7.10 shows the maps that are obtained for four distinct values of
T : T = 10, T =5, T =3and T =1.
For large values of T , the reference vectors are gathered around the center
of mass of the observation cloud. For small values of T , the neighborhood
interaction is weaker and the map is unfolded from the same initialization.
The above procedure, for a fixed value of the temperature parameter T ,
finds a local minimum of the cost function J som with respect to χ and W .
Actually, Kohonen originally suggested to repeat that minimization a num-
ber of times, with a monotonous decrease of T . In that approach, the process
performs successive steps of Fig. 7.10. The reference vectors are randomly ini-
tialized and order appears when T value is still large: the map then unfolds
until it covers the whole space of the observation distribution. The perfor-
mance of the model on completion of training, and the associated partition,
depend on the parameters of the minimization algorithm. The most important
parameters are:

• the temperature variation interval [ T min ,T max ] of the temperature para-

meter T , i.e. the initial value of T ( T max ) and its terminal value ( T min );

• the number of times N iter the iterative step is repeated;

• the cooling schedule, i.e. how T decreases in time when it spans the tem-

perature interval [ T min ,T max ].