The Performance Analysis of the Self-Stabilizing Douglas´s MCA Algorithm

The minor component (MC) is the eigenvector associated with the smallest eigenvalue of the correlation matrix of input data. In many information processing areas, it is important to online extract MC from high-dimensional input data stream. Usually, MCA learning algorithms are described by stochastic discrete time (SDT) systems and the convergence is analyzed via a corresponding DCT system, but some restrictive conditions must be satisfied in this method. The SDT method use directly the stochastic discrete learning laws to analyze the temporal behavior of MCA algorithms and some important results can be obtained. In this paper, the theoretical analysis of Douglas´s algorithm for MCA is given by using two methods: deterministic continuous time (DCT) system and stochastic discrete time system. The results of computer simulations are given to confirm the theoretical results.