Chaos control with STM of minor component analysis learning algorithm

Abstract

One of the most important techniques of feature extraction, i.e., the minor component analysis (MCA), has been widely employed in the field of data analysis. In order to meet the demands of real time computing and curtail the computational complexity, one instrument is often applied, namely, the MCA neural networks, whose learning algorithm, under some conditions, however, can produce complex dynamic behaviors, such as periodical oscillation, bifurcation, and chaos. This article introduces the chaotic dynamics theory to fully and correctly comprehend the numerical instability and chaos of iterative solutions in the MCA. Especially, as an illustration, the Douglas' MCA chaos control is discussed in details, where a stability transformation method (STM) of chaos feedback control is used in the MCA convergence control. As the time series diagrams, Jacobian matrix and Lyapunov exponent of discrete dynamic system indicate, the desired fixed points of iterative map of Douglas' MCA can be captured and the chaotic behavior of the algorithm can be controlled in the original chaotic interval.