Improvements of complex-valued Hopfield associative memory by using generalized projection rules

In this letter, new design methods for the complex-valued multistate Hopfield associative memories (CVHAMs) are presented. We show that the well-known projection rule proposed by Personnaz et al. can be generalized to complex domain such that the weight matrix of the CVHAM can be designed by using a simple and effective method. The stability of the proposed CVHAM is analyzed by using energy function approach which shows that in synchronous update mode the proposed model is guaranteed to converge to a fixed point from any given initial state. Moreover, the projection geometry of the generalized projection rule (GPR) is discussed. In order to enhance the recall capability, a strategy of eliminating the spurious memories is also reported. The validity and the performance of the proposed methods are investigated by computer simulation.