DIFFUSION-APPROXIMATION OF FREQUENCY SENSITIVE COMPETITIVE LEARNING

The focus of this paper is a convergence study of the frequency sensit ive competitive learning (FSCL) algorithm. We approximate the final ph ase of FSCL learning by a diffusion process described by a Fokker-Plan k equation. Sufficient and necessary conditions are presented for the convergence of the diffusion process to a local equilibrium. The analy sis parallels that by Ritter and Schulten for Kohonen's self-organizin g map (SOM). We show that the convergence conditions involve only the learning rate and that they are the same as the conditions for weak co nvergence described previously. Our analysis thus broadens the class o f algorithms that have been shown to have these types of convergence c haracteristics.