Self-organisation: a derivation from first principles of a class of learning algorithms

A novel derivation of T. Kohonen's topographic mapping learning algorithm is presented, which provides a simple interpretation of the role of the neighborhood update scheme which is used and prescribes a vector quantizer by minimizing an L/sub 2/ reconstruction distortion measure.

Abstract

A novel derivation of T. Kohonen's topographic mapping learning algorithm (Self-Organization and Associative Memory, Springer-Verlag, 1984) is presented. Thus the author prescribes a vector quantizer by minimizing an L/sub 2/ reconstruction distortion measure. He includes in this distribution a contribution from the effect of code noise which corrupts the output of the vector quantizer. Such code noise models the expected distorting effect of later stages of processing, and thus provides a convenient way of ensuring that the vector quantizer acquires a useful coding scheme. The neighborhood updating scheme of Kohonen's self-organizing neural network emerges as a special case of this code noise model. This reformulation of Kohonen's algorithm provides a simple interpretation of the role of the neighborhood update scheme which is used.>