Hypercomplex-valued recurrent correlation neural networks

Recurrent correlation neural networks (RCNNs), introduced by Chiueh and Goodman as an improved version of the bipolar correlation-based Hopfield network, can be used to implement high-capacity associative memories. In this paper, we extend RCNNs for processing hypercomplex-valued data. Precisely, present mathematical background a broad class RCNNs. Then, address stability new using synchronous asynchronous update modes. Examples with bipolar, complex, hyperbolic, quaternion, octonion-valued are given illustrate theoretical results. Finally, computational experiments confirm potential application memories designed storage recall gray-scale images.