A GAUSSIAN SCENARIO FOR UNSUPERVISED LEARNING

We consider random patterns on the N-sphere which are uniformly distri buted with the exception of a single symmetry-breaking orientation, al ong which they are Gaussian distributed. The unsupervised recognition of this orientation by different learning rules is studied in the larg e-N limit using the replica method. The model is simple enough to be a nalytically 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 th e upper theoretical limit imposed by the optimal (Bayes-) learning sce nario. An implementation of this algorithm is proposed and tested nume rically.