Algorithms with high order convergence speed for blind source extraction
Computational Optimization and Applications, 2007•Springer
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), p> 3, 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 …
provided and a generalization of it involving cumulants of an arbitrary order is presented. We
consider a specific optimization problem OP (p), p> 3, 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 …
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), p>3, 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−1.
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