On the discrete time dynamics of a self-stabilizing MCA learning algorithm

The stability of minor component analysis (MCA) learning algorithms is an important problem in many signal processing applications. In this paper, we propose an effective MCA learning algorithm that can offer better stability. The dynamics of the proposed algorithm are analyzed via a corresponding deterministic discrete time (DDT) system. It is proven that if the learning rate satisfies some mild conditions, almost all trajectories of the DDT system starting from points in an invariant set are bounded, and will converge to the minor component of the autocorrelation matrix of the input data. Simulation results will be furnished to illustrate the theoretical results achieved.