Projection Rule for Rotor Hopfield Neural Networks

A rotor Hopfield neural network (RHNN) is an extension of a complex-valued Hopfield neural network (CHNN). RHNNs have some excellent properties. For example, the storage capacity of an RHNN is twice that of a CHNN. The most important property of an RHNN is that it does not store rotated patterns of training patterns, unlike CHNNs, which have less noise robustness because they store rotated patterns. However, conventional learning methods for RHNNs, such as Hebbian learning rule and gradient descent learning rules, present difficulties with regard to, for example, storage capacity, noise robustness, and learning time. In this paper, we propose a projection rule for RHNN and demonstrate that the noise robustness of RHNN is better than that of CHNN. The proposed algorithm improves the noise robustness of RHNN. As the number of training patterns increases, the noise robustness of CHNN rapidly deteriorates. On the other hand, the noise robustness of RHNN reduces less rapidly for the same case. Moreover, RHNN can easily recover from rotated patterns, unlike CHNN. We show this ability by computer simulation.