A Gaussian scenario for unsupervised learning

Abstract

We consider random patterns on the N-sphere which are uniformly distributed with the exception of a single symmetry-breaking orientation, along which they are Gaussian distributed. The unsupervised recognition of this orientation by different learning rules is studied in the large-N limit using the replica method. The model is simple enough to be analytically tractable and rich enough to exhibit most of the phenomena observed with other pattern distributions. A learning algorithm based on the minimization of a cost function is identified which reaches the upper theoretical limit imposed by the optimal (Bayes-) learning scenario. An implementation of this algorithm is proposed and tested numerically.