Dynamical Systems for Principal Singular Subspace Analysis

Abstract

The computation of the principal subspaces is an essential task in many signal processing and control applications. In this paper novel dynamical systems for finding the principal singular subspace and/or components of arbitrary matrix are developed. The proposed dynamical systems are gradient flows or weighted gradient flows derived from the optimization of certain objective functions over orthogonal constraints. Global asymptotic stability analysis and domains of attractions of these systems are examined via Liapunov theory and LaSalle invariance principle. Weighted versions of these methods for computing principal singular components are also given. Qualitative properties of the proposed systems are analyzed in detail