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Self-Normalizing Dual Systems for Minor and Principal Component Extraction

In this paper classes of globally stable dynamical systems for dual-purpose extraction of principal and minor components are analyzed. The proposed systems may apply to both the standard and the generalized eigenvalue problems. Lyapunov stability theory and LaSalle invariance principle are used to derive invariant sets for these systems. Some of these systems may be viewed as generalizations of known learning rules such as Oja's and Xu's systems and are shown to be applied, with some modifications, to symmetric and nonsymmetric matrices. Numerical examples are provided to examine the convergence behavior of the dual-purpose minor and principal component analyzers.