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Stability and chaos of LMSER PCA learning algorithm

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  • Lv, Jian Cheng
  • Yi, Zhang

Abstract

LMSER PCA algorithm is a principal components analysis algorithm. It is used to extract principal components on-line from input data. The algorithm has both stability and chaotic dynamic behavior under some conditions. This paper studies the local stability of the LMSER PCA algorithm via a corresponding deterministic discrete time system. Conditions for local stability are derived. The paper also explores the chaotic behavior of this algorithm. It shows that the LMSER PCA algorithm can produce chaos. Waveform plots, Lyapunov exponents and bifurcation diagrams are presented to illustrate the existence of chaotic behavior of this algorithm.

Suggested Citation

  • Lv, Jian Cheng & Yi, Zhang, 2007. "Stability and chaos of LMSER PCA learning algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1440-1447.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:4:p:1440-1447
    DOI: 10.1016/j.chaos.2005.11.076
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    1. Jing, Zhujun & Yang, Jianping, 2006. "Bifurcation and chaos in discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 259-277.
    2. Wang, Xuedi & Tian, Lixin, 2006. "Bifurcation analysis and linear control of the Newton–Leipnik system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 31-38.
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