Chaos control of LMSER principal component analysis learning algorithm

LMSER (least mean square error reconstruction) PCA (principal component analysis) algorithm is a learning algorithm which is generally used to extract principal components of data. However, the algorithm can produce complicated dynamical behavior under certain conditions, such as the periodic oscillation, bifurcation and chaos. This paper introduces the chaos control of LMSER PCA, and the stability transformation method (STM) of chaos feedback control is specifically applied to the convergence control of LMSER PCA. Time series diagrames, Lyapunov exponent of discrete dynamical system of PCA illustrate that the desired fixed points of iterative map of LMSER PCA can be captured, and the chaotic behavior of LMSER PCA can be controlled.