The Basic SOM

We shall now demonstrate a very important phenomenon that apparently has a close relationship to the brain maps discussed in Sect. 2.12 and occurs in certain spatially interacting neural networks. While being categorizable as a special kind of adaptation, this phenomenon is also related to regression. In regression, some simple mathematical function is usually fitted to the distribution of sample values of input data. The “nonparametric regression” considered in this chapter, however, involves fitting a number of ordered discrete reference vectors, similar to the codebook vectors discussed in Sect. 1.4.2, to the distribution of vectorial input samples. In order to approximate continuous functions, the reference vectors are here made to define the nodes of a kind of hypothetical “elastic network,” whereby the topological order characteristic of this mapping, and a certain degree of regularity of the neighboring reference vectors ensue from their local interactions, reflecting a kind of “elasticity.” One possibility to implement such an “elasticity” would be to define the local interactions between the nodes in the signal space [3.1 — 7], whereas more realistic spatial interactions, from a neural modeling point of view, are definable between the neurons along the neural network. The latter approach is mainly made in this text.

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