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