An Effective Principal Singular Feature Information Extracting Algorithm

In this paper, a effective algorithm to effectively estimate the singular component and value from the cross-covariance kind of matrix from two data streams by using the neural network approach. Different from traditional algorithms, the newly proposed algorithm can estimate not only the principal singular vectors (PSVRs) but also the principal singular values (PSVEs). First, a dynamical system is obtained from the gradient flow, which is obtained from the optimization of a novel information criterion. Then, based on the dynamical system, a stable neural network algorithm, which can extract the left and right PSVRs, is obtained. Moreover, the PSVE can also be obtained based on the estimated left or (and) right singular vectors (SVRs), because the norm of the SVRs mainly depends on the corresponding singular value (SVE) of the cross-covariance matrix. In this case, the principal singular triplet (PST, PSVRs and the corresponding SVE) of the cross-covariance matrix can be extracted by using the algorithm proposed in this paper. What's more, the algorithm proposed in this paper can also be used for multiple PSTs extractions on the basis of the sequential method. Then, the convergence of the algorithm is analyzed, and the result illustrates that the algorithm proposed in this paper converges to the stable equilibrium point with probability 1. Last, experiment results show that the algorithm proposed in this paper is fast and stable in convergence, and can also extract multiple PSTs efficiently.