Symmetric quaternionic Hopfield neural networks

Quaternion algebra is an extension of complex number system and has the property of non-commutativity. Quaternionic Hopfield neural networks (QHNNs) are extensions of complex-valued Hopfield neural networks (CHNNs) using quaternions, and several models have been proposed. Both the CHNNs and QHNNs have low noise tolerance due to rotational invariance. Recently, a novel CHNN model, a symmetric CHNN (SCHNN), has been proposed to improve noise tolerance of CHNNs. In the present work, this scheme is extended to the QHNNs. The proposed model is referred to as a symmetric QHNN (SQHNN). We show that the SQHNNs improve the noise tolerance by computer simulations.