Correlation Matrix Memories

A new model for associative memory, based on a correlamatrix, and the rest of the elements are put equal to zero. In tion matrix, is suggested. In this model information is accumulated on a t ~~~~~~~~~~~~~addition to such a ranldomly sam led matrix, we discuss a memory elements as products of component data. Denoting a key vector by q(P), and the data' associated with it by another vector x(P), the pairs randomly generated associative network in which a set of (q(P), x(")) are memorized in the form of a matrix memory elements is interconnected at random to two input cEx(P)q(P) = Mxq elements. If the number of memory elements is sufficiently P large, this model still reconstructs information stored in it. where c is a constant. A randomly selected subset of the elements of Mxq Such a matrix is both failure tolerant, and completely rancan also be used for memorizing. The recalling of a particular datum x(r is made by a transformation x(r) Mxqq(r). This model is failure domly organized. tolerant and facilitates associative search of information; these are properIn this paper, after setting up the structure of the model, ties that are usually assigned to holographic memories. Two classes of we will make a formal mathematical approach to the probmemories are discussed: a complete correlation matrix memory (CCMM)i, s n o t and randomly organized incomplete correlation matrix memories (ICMM). em In which the analyzed. The data recalled from the latter are stochastic variables but the fidelity of recall is shown to have a deterministic limit if the number of memory The Model elements grows without limits. A special case of correlation matrix memories is the auto-associative memory in which any part of the memoThe correlation matrix model has the structure depicted rized information can be used as a key. The memories are selective with in Fig. 1. Here we have an input field which consists of two respect to accumulated data. The ICMM exhibits adaptive improvement under certain circumstances. It is also suggested that correlation matrix .prts:t setf ut elem e enod by and se memories could be applied for the classification of data. comprises a keyfield used for the encoding of data, and the set denoted by an index set J is a data field. All input ele