DocumentCode :
1486005
Title :
Superefficiency in blind source separation
Author :
Amari, Shun-Ichi
Author_Institution :
RIKEN, Inst. of Phys. & Chem. Res., Saitama, Japan
Volume :
47
Issue :
4
fYear :
1999
fDate :
4/1/1999 12:00:00 AM
Firstpage :
936
Lastpage :
944
Abstract :
Blind source separation is the problem of extracting independent signals from their mixtures without knowing the mixing coefficients nor the probability distributions of source signals and may be applied to EEG and MEG imaging of the brain. It is already known that certain algorithms work well for the extraction of independent components. The present paper is concerned with superefficiency of these based on the statistical and dynamical analysis. In a statistical estimation using t examples, the covariance of any two extracted independent signals converges to 0 of the order of 1/t. On-line dynamics shows that the covariance is of the order of η when the learning rate η is fixed to a small constant. In contrast with the above general properties, a surprising superefficiency holds in blind source separation under certain conditions where superefficiency implies that covariance decreases in the order of 1/t2 or of η2 . The paper uses the natural gradient learning algorithm and method of estimating functions to obtain superefficient procedures for both batch estimation and on-line learning. A standardized estimating function is introduced to this end. Superefficiency does not imply that the error variances of the extracted signals decrease in the order of 1/t2 or η2 but implies that their covariances (and independencies) do
Keywords :
convergence of numerical methods; covariance analysis; electroencephalography; feature extraction; gradient methods; magnetoencephalography; medical image processing; probability; EEG imaging; MEG imaging; batch estimation; blind source separation; brain; convergence; covariance; dynamical analysis; error variances; function estimation; independent signals extraction; learning rate; mixing coefficients; mixtures; natural gradient learning algorithm; on-line dynamics; probability distributions; source signals; standardized estimating function; statistical analysis; statistical estimation; superefficiency; Blind source separation; Covariance matrix; Data mining; Electroencephalography; Entropy; Error analysis; Independent component analysis; Probability distribution; Source separation; Stability analysis;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.752592
Filename :
752592
Link To Document :
بازگشت