A Novel Continuous-Valued Quaternionic Hopfield Neural Network

In this paper, we introduce a kind of Hopfield network that can be used for the storage and recall of vectors whose entries are unit quaternion´s. We show that the novel model, referred to as continuous-valued quaternion Hopfield neural network (CV-QHNN), produces a sequence that under mild conditions converges to a fixed point for any initial state. Furthermore, computational experiments reveal that a CV-QHNN, synthesized using the projection rule, exhibit optimal absolute storage capacity and some noise tolerance as an associative memory model.