Self-Organizing Maps and Unsupervised Classification - Neural Networks: Methodology and Applications - page 411

Fig. 7.15. Comparison k -means ( a ) and SOM ( b ) for the same initialization. The
reference vectors are initialized in the right bottom of the picture

that solution is different from the solution that was found by the straight-
forward implementation of k -means (Fig. 7.15 [a]). To summarize, the map
provided a better representation of the training set.

Fig. 7.16. Modeling of the SOM according to a probability density mixture. The
map is shown in the neural formalism: 3 layer architecture: an input layer and two
layers that are maps with similar size and similar topology. A neuron of C 1 represents
a gaussian with expectation vector w c and scalar covariance matrix σ c I ; a neuron of
C 2 represents a Gaussian mixture, whose density is given by p ( z )= c 2 p ( c 2 ) p c 2 ( z )

where p c 2 ( z )= c 1 p ( c 1 | c 2 ) p ( z | c 1 )