John A. Flanagan | Search PubMed

PubMed1997

Analysing a Self-organising Algorithm.

A self-organising algorithm is described, which is a generalisation of an algorithm proposed by Cottrell and Fort. The algorithm is analysed in a more general fashion using the ordinary differential equation method (ODE) of stochastic approximation theory. The results is a set of linear equations which the stationary state of the neuron weights must satisfy. Several features of the algorithm are analysed including the conditions necessary for the existence of a single stationary point as well as the configuration of the stationary state. It is shown what conditions favour the convergence of the neuron weights towards an organised configuration. Copyright 1997 Elsevier Science Ltd.

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PubMed1996

Self-organisation in Kohonen's SOM.

Self-organisation in Kohonen's self-organising map (SOM) is analysed by considering the neuron weights to be a Markov process. While many works exist which analyse the one-dimensional SOM, the aim of the study is to demonstrate probability one convergence of the neuron weights to an organised configuration in one- and also in higher-dimensional SOMs.A proof of self-organisation is given for the one-dimensional case for a general type of probability distribution satisfying conditions given in terms of the parameters of the network. A modified version of the SOM algorithm is described which has an absorbing organised configuration, even in higher dimensions. Probability one convergence to this configuration is demonstrated. The higher-dimensional SOM is also analysed and it is shown for certain conditions that the first entry time of the neuron weights into a predefined organised state is finite with probability one. Copyright 1996 Elsevier Science Ltd

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