Principal components and pattern storage in a fully connected net
Stephen Coombes, JG Taylor · 1995
We 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. We present simulation results that show these connections are 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 those of the Psuedo-Inverse rule. Finally, we discuss a biologically plausible method of constructing such a connection matrix. 1 Introduction The fully connected net (Hopfield 1982) is a model of a neural network which exhibits associative memory (Amit 1989). It consists of a connected system of spins (neurons), s i = \\Sigma1, with adaptable internal connections (synapses) w ij ; i; j = 1; 2; 3 : : :N . The synapses are chosen such that a prescribed set of states become fixed point attractors of the network dynamics. These states f j = 1; 2; 3 : : :Pg are the patterns m...