Two-level quaternion-valued Hopfield networks

Abstract

A complex-valued Hopfield network (CHN) is a multistate model of Hopfield neural network and has been applied to storage of image data. A two-level CHN (TLCHN) was proposed as a noise robust model against Gaussian noise. The disadvantage is that it has four times as many weight parameters as a CHN. To reduce the number of weight parameters, we propose a two-level quaternion-valued Hopfield network (TLQHN). A TLQHN has half weight parameters of TLCHN. A TLCHN improves the noise tolerance against Gaussian noise by the strength parameter, which is incorporated in the weight parameters. In a TLQHN, the strength parameter is hardly incorporated in the weight parameters, unlike a TLCHN. Instead, the strength parameter is incorporated in the weighted sum input. Computer simulations using image data show that the TLQHNs provide better noise tolerance than the models with same number of weight parameters.