Stochastic competitive learning

The probabilistic foundations of competitive learning systems are developed. Continuous and discrete formulations of unsupervised, supervised, and differential competitive learning systems are studied. These systems estimate an unknown probability density function from random pattern samples and behave as adaptive vector quantizers. Synaptic vectors in feedforward competitive neural networks quantize the pattern space and converge to pattern class centroids or local probability maxima. The stochastic calculus and a Lyapunov argument prove that competitive synaptic vectors converge to centroids exponentially quickly. Convergence does not depend on a specific dynamical model of how neuronal activations change