Affiliations: Institute of Mathematics, Polish Academy of Sciences | Faculty of Electronics and Information Technology, Warsaw University of Technology Address: Nowowiejska 15/19, 00-665 Warszawa, POLAND. Email: Skarbek@ire.pw.edu.pl
Note: [] Address for correspondence: Institute of Mathematics, Polish Academy of Science, Warsaw, Sniadeckich 8
Note: [] Address for correspondence: Faculty of Electronics and Information Technology, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warsaw, Poland
Abstract: It is shown that the discrete time dynamical system defined by the Oja-RLS algorithm is stable in the closed ring K(0,9/8) – $\overline{K}$(0,8/9) if only the initial gain β0 is bounded by (2B)−1, where B = b2 and b is the bound for the learning sequence. It is rigorously proved that automatically computed gains βn in Oja-RLS scheme converge to zero with the rate 1/n, almost surely.
Keywords: KLT transform, Principal Component Analysis, OJA-RLS learning scheme, stability of neural algorithm
