Analysis of classification performance for Hopfield network with predefined correlated exemplar patterns

The classification performance after a single iteration is derived as a function of the number of exemplar patterns, the number of processing elements in the network, input bit error probability, and inner-product values among exemplar patterns. It is shown that, when the exemplar patterns are orthogonal with each other, the correlations among the weighted sums are nothing but constant multiples of the weights. These values are rarely zero, which makes the analysis complex. However, the values of correlation reduce greatly when these weighted sums pass through the threshold. The classification performances after single and multiple iterations are derived using this method and compared with simulation results. The results can be a valuable reference in the design of Hopfield-type associative memories