Stochastic analysis and comparison of Kohonen SOM with optimal filter

In this paper a detailed investigation of the statistical and convergent properties of Kohonen´s self-organising map (SOM) algorithm is presented. The central limit theorem has been extended and then applied to prove that the feature space in SOM learning is an approximation to Gaussian distributed stochastic processes, and will eventually converge in the mean-square sense to the density centres of the input probabilistic sub-domains. We demonstrate that by combining the SOM with a Kalman filter will smooth and accelerate the learning and convergence of the SOM, especially in early training stages. We also present a discussion on the local optimisation problem of the SOM algorithm