New Dynamical Systems for Principal and Minor Subspace Analysis

New dynamical systems for extracting multiple principal and minor components of a square matrix are presented. Analyses for determining invariant sets, domains of attraction and asymptotic stability of these systems are provided. These systems can be slightly modified so that they converge to the actual eigen or singular vectors by incorporating a diagonal matrix having distinct eigenvalues. Some of the proposed algorithms generalize known systems such as Oja´s systems for principal and minor component analysis and are derived from optimizing bounded function over compact sets. Dual purpose systems for computing minor and principal component analyzers are also derived. Additionally, exact solutions for some non-linear learning dynamical systems are given