Convergence properties of a class of learning vector quantization algorithms

A mathematical analysis of a class of learning vector quantization (LVQ) algorithms is presented. Using an appropriate time-coordinate transformation, we show that the LVQ algorithms under consideration can be transformed into linear time-varying stochastic difference equations. Using this fact, we apply stochastic Lyapunov stability arguments, and we prove that the LVQ algorithms under consideration do indeed converge, provided that some appropriate conditions hold.