Convergence analysis of the OJAn MCA learning algorithm by the deterministic discrete time method

Authors:
Dezhong Peng;Zhang Yi
Affiliations:
Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, PR China;Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, PR China
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

Minor component analysis (MCA) is a statistical method of extracting the eigenvector associated with the smallest eigenvalue of the covariance matrix of input signals. Convergence is essential for MCA algorithms towards practical applications. Traditionally, the convergence of MCA algorithms is indirectly analyzed via their corresponding deterministic continuous time (DCT) systems. However, the DCT method requires the learning rate to approach zero, which is not reasonable in many applications due to the round-off limitation and tracking requirements. This paper studies the convergence of the deterministic discrete time (DDT) system associated with the OJAn MCA learning algorithm. Unlike the DCT method, the DDT method does not require the learning rate to approach zero. In this paper, some important convergence results are obtained for the OJAn MCA learning algorithm via the DDT method. Simulations are carried out to illustrate the theoretical results achieved.