A novel approach to design weight matrix of Hopfield network

The sum of outer product learning rule is a traditional method to generate the weight matrix of Hopfield network. It requires all of the samples to be pairwise orthogonal, which is difficult to achieve in general conditions. In this paper, a novel approach to design the weight matrix is proposed, and it just requires samples to be linearly independent that is easy to carry out. As we all know, a group of linearly independent vectors can be transferred to a group of standard orthogonal vectors. Thus, we can construct weight matrix W using these standard orthogonal vectors instead of original samples. Experimental results demonstrate that the new approach can help to achieve an ideal auto-association performance.