A Cascade Neural Network for Blind Signal Extraction without Spurious Equilibria

Ruck THAWONMAS  Andrzej CICHOCKI  Shun-ichi AMARI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E81-A   No.9   pp.1833-1846
Publication Date: 1998/09/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
Category: Neural Networks
blind source separation and extraction,  neural networks,  on-line adaptive algorithms,  

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We present a cascade neural network for blind source extraction. We propose a family of unconstrained optimization criteria, from which we derive a learning rule that can extract a single source signal from a linear mixture of source signals. To prevent the newly extracted source signal from being extracted again in the next processing unit, we propose another unconstrained optimization criterion that uses knowledge of this signal. From this criterion, we then derive a learning rule that deflates from the mixture the newly extracted signal. By virtue of blind extraction and deflation processing, the presented cascade neural network can cope with a practical case where the number of mixed signals is equal to or larger than the number of sources, with the number of sources not known in advance. We prove analytically that the proposed criteria both for blind extraction and deflation processing have no spurious equilibria. In addition, the proposed criteria do not require whitening of mixed signals. We also demonstrate the validity and performance of the presented neural network by computer simulation experiments.