Analysis of Dynamical Systems for Generalized Principal and Minor Component Extraction

In this paper globally stable dynamical systems for the standard and the generalized eigenvalue problem are developed. These systems may be viewed as generalizations of known learning rules applied to nondefinite and/or nonsymmetric matrices. We also modified the original Oja's systems to obtain new dynamical systems with a larger domain of attraction. For certain class of matrices which satisfy positive definiteness condition, the modified rules are globally stable. The convergence behavior has been examined to identify the stationarity conditions, stability conditions, and domains of attraction for some of these systems