An Effective Neural Learning Algorithm for Extracting Cross-Correlation Feature Between Two High-Dimensional Data Streams

摘要

A novel information criterion for principal singular subspace tracking is proposed and a corresponding principal singular subspace gradient flow is derived based on the information criterion in this paper. The information criterion exhibits a unique global minimum attained if and only if the state matrices of the left and right neural networks span the left and right principal singular subspace of a cross-correlation matrix between two high-dimensional vector sequences, respectively. The proposed gradient flow can efficiently track an orthonormal basis of the principal singular subspace, and it has fast convergence speed, good suitability for data matrix close to singular matrix and excellent self-stabilizing property. The global asymptotic stability and self-stabilizing property of the proposed algorithm are analyzed. The simulation experiments validate the excellent performance of the proposed algorithm.