A new method to build an associative memory model

Abstract

An associative memory is an artificial neural network model designed to store and recall input-output patterns pairs by association. A new method for obtaining two associative memories +M and -M is presented in this article, which uses a framework focused on two new binary operations boxplus and boxminus, and a unary operation called projection. The conditions to obtaining perfect recovery and the noise boundaries that the memories can tolerate are studied. Memories +M and -M are robust to additive and subtractive noise, respectively, both types converge in one-step and operate in heteroassociative and autoassociative modes. The performance of the proposed memories is tested against other memory models under identical conditions using the gamma binary distance for measuring similarity between binary patterns. The computer simulation results based on the average of 500 trials with the binary set of 26 lowercase letters of 7x7 pixel size, showed that the proposed memories in autoassociative mode exhibited a gamma binary distance of above .8, .75 and .7 by distorting up to 10 pixels by additive, subtractive, and mixed noise, respectively, which implied that the recovered images had a high similarity. In absence of noise the performance was excellent, i.e., the 100% of the recovered images were identical.