On Stability of Oja Algorithm
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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.
KeywordsLearning Sequence Stochastic Approximation Discrete Dynamical System Principal Vector Digit Recognition
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