Convergence analysis of a simple minor component analysis algorithm.

Abstract

Minor component analysis (MCA) is a powerful statistical tool for signal processing and data analysis. Convergence of MCA learning algorithms is an important issue in practical applications. In this paper, we will propose a simple MCA learning algorithm to extract minor component from input signals. Dynamics of the proposed MCA learning algorithm are analysed using a corresponding deterministic discrete time (DDT) system. It is proved that almost all trajectories of the DDT system will converge to minor component if the learning rate satisfies some mild conditions and the trajectories start from points in an invariant set. Simulation results will be furnished to illustrate the theoretical results achieved.