On the Effect of Noise on the Moore-Penrose Generalized Inverse Associative Memory

Monte Carlo simulations of the continuous Moore-Penrose generalized inverse associative memory (Kohonen [l]) have shown that the noise-to-signal ratio is improved on recall in the autoassociative case as long as the number of vector pairs stored is less than the number of components per vector. In the heteroassociative case, however, the noise-to-signal ratio may actually be greatly increased upon recall, particularly as the number of vector pairs stored approaches the number of components per vector. The increase in output noise-to-signal ratio in the heteroassociative case is found to be due to the fact that the inverse of the product of the key vector matrix with its transpose may increase without bound in spite of the fact that the key vectors are linearly independent.