Abstract

One of the many possible conditions for pattern storage in a Hopfield net is to demand that the local field vector be a pattern reconstruction. We use this criterion to derive a set of weights for the storage of correlated biased patterns in a fully connected net. The connections are built from the eigenvectors or principal components of the pattern correlation matrix. Since these are often identified with the features of a pattern set we have named this particular set of weights as the feature matrix. We present simulation results that show the feature matrix to be capable of storing up to N random patterns in a network of N spins. Basins of attraction are also investigated via simulation and we compare them with both our theoretical analysis and those of the pseudo-inverse rule. A statistical mechanical investigation using the replica trick confirms the result for storage capacity. Finally we discuss a biologicaly plausible learning rule capable of realising the feature matrix in a fully connected net. Copyright © 1996 Elsevier Science Ltd

Author Keywords: Hopfield networks, Principal component analysis, Statistical mechanics

^*Requests for reprints should be sent to Dr Stephen Coombes, Neural Computing Research Group, Department of Engineering Maths, Queens Building, University Walk, University of Bristol, Bristol, BS8 1TR, UK; e-mail: S.Coombes@Bristol.ac.uk