Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the CramÉr-Rao Lower Bound

FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm whi...

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Bibliographic Details
Published in:IEEE transactions on neural networks Vol. 17; no. 5; pp. 1265 - 1277
Main Authors: Koldovsky, Z., Tichavsky, P., Oja, E.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.09.2006
Institute of Electrical and Electronics Engineers
Subjects:
Algorithm FastICA
Algorithms
Applied sciences
Artificial Intelligence
Asymptotic properties
Automation
blind deconvolution
blind source separation
Computational complexity
Computational modeling
Computer science; control theory; systems
Computer Simulation
Computing Methodologies
Connectionism. Neural networks
CramÉr-Rao lower bound (CRB)
Data Interpretation, Statistical
Deconvolution
Errors
Exact sciences and technology
Independent component analysis
independent component analysis (ICA)
Information theory
Lower bounds
Matlab
Models, Statistical
Neural networks
Pattern Recognition, Automated - methods
Principal Component Analysis
Probability distribution
Signal processing
Signal processing algorithms
Signal Processing, Computer-Assisted
Speech
Source separation
Cramér-Rao lower bound (CRB)
independent component analysis (ICA)
Independent component analysis
Error bound
Blind deconvolution
Neural network
Computational complexity
Algorithm FastICA
blind source separation
Algorithm analysis
Blind separation
ISSN:1045-9227, 1941-0093
Online Access:Get full text
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Summary:FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm which is asymptotically efficient, i.e., its accuracy given by the residual error variance attains the Cramer-Rao lower bound (CRB). The error is thus as small as possible. This result is rigorously proven under the assumption that the probability distribution of the independent signal components belongs to the class of generalized Gaussian (GG) distributions with parameter alpha, denoted GG(alpha) for alpha>2. We name the algorithm efficient FastICA (EFICA). Computational complexity of a Matlab implementation of the algorithm is shown to be only slightly (about three times) higher than that of the standard symmetric FastICA. Simulations corroborate these claims and show superior performance of the algorithm compared with algorithm JADE of Cardoso and Souloumiac and nonparametric ICA of Boscolo on separating sources with distribution GG(alpha) with arbitrary alpha, as well as on sources with bimodal distribution, and a good performance in separating linearly mixed speech signals
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ISSN:1045-9227
1941-0093
DOI:10.1109/TNN.2006.875991