Monotonic convergence of fixed-point algorithms for ICA

We re-examine a fixed-point algorithm proposed by Hyvarinen for independent component analysis, wherein local convergence is proved subject to an ideal signal model using a square invertible mixing matrix. Here, we derive step-size bounds which ensure monotonic convergence to a local extremum for an...

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Bibliographic Details
Published inIEEE transactions on neural networks Vol. 14; no. 4; pp. 943 - 949
Main Authors Regalia, P.A., Kofidis, E.
Format Journal Article
LanguageEnglish
Published United States IEEE 01.07.2003
Institute of Electrical and Electronics Engineers
Subjects
Algorithms
Appeals
Background noise
Convergence
Engineering Sciences
Fixed points (mathematics)
Image restoration
Independent component analysis
Information processing
Initial conditions
Mathematical models
Neural networks
Probability density function
Random variables
Sensors
Signal analysis
Signal and Image processing
Signal restoration
Vectors
Non-Gaussian signals
Fixed-point algorithms
Monotonic convergence
Independent component analysis (ICA)
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Summary:We re-examine a fixed-point algorithm proposed by Hyvarinen for independent component analysis, wherein local convergence is proved subject to an ideal signal model using a square invertible mixing matrix. Here, we derive step-size bounds which ensure monotonic convergence to a local extremum for any initial condition. Our analysis does not assume an ideal signal model but appeals rather to properties of the contrast function itself, and so applies even with noisy data and/or more sources than sensors. The results help alleviate the guesswork that often surrounds step-size selection when the observed signal does not fit an idealized model.
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ISSN:1045-9227
1941-0093
DOI:10.1109/TNN.2003.813843