Quaternionic Recurrent Correlation Neural Networks
Marcos Eduardo Valle · 2018
In this paper, we introduce the class of quaternionic recurrent correlation neural networks (QRCNNs), which extended the real-valued bipolar recurrent correlation neural networks of Chiueh and Goodman using unit quaternions. We show that the QRCNNs always settle down at an equilibrium independently of the initial state. Also, we address the absolute storage capacity and error correction capability of the QRCNN as associative memory models. Precisely, we prove that if the activation function of the hidden layer is an exponential on its parameter, then the QRCNN with a sufficiently large parameter is able to implement an associative memory. Moreover, the radius of the basis of attraction of the resulting associative memory is at least half the Euclidean distance between the two closest fundamental memories. Computational experiments are provided to illustrate the theoretical results.