Transformations between left and right quaternion-valued neural networks

Abstract

Hopfield networks have been studied as neural associative memories by many researchers. Classic Hopfield networks have been extended to high-dimensional models. Complex-valued Hopfield networks are most successful extensions and have been applied to multistate associative memories. Quaternion-valued Hopfield networks (QVHNs) are also such models. Left and right QVHNs are different models, since the multiplication of quaternions is not commutative. This work provides the transformations between the left and right QVHNs. The software for one type of QVHNs is available for the other type of QVHNs through the transformations. The learning algorithms, such as hebbian and projection rules, are also transformed. In addition, we reveal the relations between the left and right QVHNs. This theory is available for the quaternion-valued MLPs (QVMLPs). In fact, we provide the implementation of right QVMLPs using the left QVMLPs.