Algorithms with high order convergence speed for blind source extraction

Authors:
Pando Georgiev;Panos Pardalos;Andrzej Cichocki
Affiliations:
ECECS Department, University of Cincinnati, Cincinnati, USA 45221-0030 and Sofia University "St. Kl. Ohridski", Sofia, Bulgaria 1164;Center for Applied Optimization, University of Florida, Florida, USA;The Institute for Physical and Chemical Research (RIKEN), Brain Science Institute, Saitama, Japan 351-0198
Venue:
Computational Optimization and Applications
Year:
2007

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Abstract

A rigorous convergence analysis for the fixed point ICA algorithm of Hyvärinen and Oja is provided and a generalization of it involving cumulants of an arbitrary order is presented. We consider a specific optimization problem OP(p), p3, integer, arising from a Blind Source Extraction problem (BSE) and prove that every local maximum of OP(p) is a solution of (BSE) in sense that it extracts one source signal from a linear mixture of unknown statistically independent signals. An algorithm for solving OP(p) is constructed, which has a rate of convergence p驴1.