An Effective Principal Singular Triplets Extracting Neural Network Algorithm

摘要

In this paper, we propose an effective neural network algorithm to perform singular value decomposition (SVD) of a cross-correlation matrix between two data streams. Different from traditional algorithms, the newly proposed algorithm can extract not only the principal singular vectors but also the corresponding principal singular values. First, a dynamical system is obtained from the gradient flow, which is obtained from optimization of a novel information criterion. Then, based on the dynamical system, a stable neural network algorithm, which can extract the left and right principal singular vectors, is obtained. Moreover, by satisfying orthogonality instead of orthonormality, we are able to extract the normalization scale factor as the corresponding singular value. In this case, the principal singular triplet (principal singular vectors and the corresponding singular value) of the cross-correlation matrix can be extracted by using the proposed algorithm. What’s more, the proposed algorithm can also be used for multiple PSTs extraction on the basis of sequential method. Then, convergence analysis shows that the proposed algorithm converges to the stable equilibrium point with probability 1. Last, experiment results show that the proposed algorithm is fast and stable in convergence, and can also extract multiple PSTs efficiently.