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Convergence analysis of Chauvin’s PCA learning algorithm with a constant learning rate

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  • Lv, Jian Cheng
  • Yi, Zhang

Abstract

The convergence of Chauvin’s PCA learning algorithm with a constant learning rate is studied in this paper by using a DDT method (deterministic discrete-time system method). Different from the DCT method (deterministic continuous-time system method), the DDT method does not require that the learning rate converges to zero. An invariant set of Chauvin’s algorithm with a constant learning rate is obtained so that the non-divergence of this algorithm can be guaranteed. Rigorous mathematic proofs are provided to prove the local convergence of this algorithm.

Suggested Citation

  • Lv, Jian Cheng & Yi, Zhang, 2007. "Convergence analysis of Chauvin’s PCA learning algorithm with a constant learning rate," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1562-1571.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:4:p:1562-1571
    DOI: 10.1016/j.chaos.2005.12.007
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    References listed on IDEAS

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    1. Arik, Sabri, 2005. "Global robust stability analysis of neural networks with discrete time delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1407-1414.
    2. Tu, Fenghua & Liao, Xiaofeng, 2005. "Estimation of exponential convergence rate and exponential stability for neural networks with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1499-1505.
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