Characterization of first and second order Hopfield neural networks

The characteristics of two types of Hopfield binary autoassociative memories (HMs) are explored. These two HMs are: (1) the binary correlation (or first order) version, i.e., the original Hopfield model, (2) the quadratic correlation (or second order) version. The existence of a signal-to-noise ratio parameter useful for determining the characteristics of these two HMs has been proposed. This constant parameter obtained from signal-to-noise ratio calculations leads to a variety of equations which have been found capable of concisely estimating the storage capacity, convergence probability and attraction radii of these two HMs. The validity of these equations is evaluated through comparisons with simulation results presented in this thesis The comparisons between these two HMs in terms of storage capacity and attraction radius are also investigated.