On Stability of Oja Algorithm

Authors:
Radoslaw Sikora;Wladyslaw Skarbek
Affiliations:
-;-
Venue:
RSCTC '98 Proceedings of the First International Conference on Rough Sets and Current Trends in Computing
Year:
1998

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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 βn are bounded by (2B)-1; where B = b2 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.