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Neural Network Associative Memories and Input Space With Non-Orthonormal Basis

One of the main problems with using Neural Network Associative Memories appears when the signals to be learned determine a non-orthogonal basis. In dealing with this type of basis, an error is introduced in the association and, because of this, a perfect matching is not obtained. Based in theoretical considerations only, this paper addresses the problem of getting rid cross-talk terms in the final recalling of an autoassociative neural network when input patterns belong to a subspace embedded into the whole input pattern space. One of the methods obtained also considers optimization in matrix weight size, at the expense of redefining the weight matrix, the activation function and the output space. Particularly interesting results the fact that we get rid of the cross-talk term by just considering one-single layer heteroassociative-competitive neural network defined on the subspace generated by the set of linearly independent input patterns. The results are very important in practical questions such as image and pattern recognition, as well.