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.

在本文中，我们提出了一种有效的神经网络算法来执行两个数据流之间互相关矩阵的奇异值分解（SVD）。与传统算法不同，新提出的算法不仅可以提取主奇异矢量，还可以提取对应的主奇异值。首先，从梯度流中获得动力系统，该梯度系统是从新型信息准则的优化中获得的。然后，基于动力学系统，获得了一种稳定的神经网络算法，可以提取左右主奇异向量。此外，通过满足正交性而不是正交性，我们能够提取归一化比例因子作为相应的奇异值。在这种情况下，利用所提出的算法，可以提取互相关矩阵的主奇异三元组（主奇异矢量和相应的奇异值）。此外，该算法还可以在顺序法的基础上用于多个PST的提取。然后，收敛性分析表明，该算法收敛到稳定平衡点的概率为1。最后，实验结果表明，该算法收敛速度快，稳定，并且可以有效地提取多个PST。