Quaternionic Vector Product Hopfield Network

Abstract

A vector product Hopfield network (VPHN) is a 3-D Hopfield model. A VPHN provides excellent noise tolerance. Since projection rule is not available, it is not applicable for large numbers of data. Vector product appears in the multiplication of quaternions. In this work, the VPHNs are extended to the quaternionic VPHNs (QVPHNs). The projection rule is available for the QVPHNs. We evaluate the QVPHNs by computer simulations and show that they provide excellent noise tolerance.