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On Stability of Oja Algorithm

  • Radosław Sikora
  • Władysław Skarbek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1424)

Abstract

By elementary tools of matrix analysis, we show that the discrete dynamical system defined by Oja algorithm is stable in the ball K(0,81/64) if only gains β n are bounded by (2B)−1, where B = b 2 and b is the bound for the learning sequence. We also define a general class of Oja’s systems (with gains satisfying stochastic convergence conditions) which tend to the infinity with exponential rate if only their initial states are chosen too far from the zero point.

Keywords

Learning Sequence Stochastic Approximation Discrete Dynamical System Principal Vector Digit Recognition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Radosław Sikora
    • 1
  • Władysław Skarbek
    • 2
  1. 1.Institute of MathematicsPolish Academy of SciencesPoland
  2. 2.Department of Electronics and Information TechnologyWarsaw University of TechnologyWarsaw

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