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Monotonic convergence of fixed-point algorithms for ICA

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2 Author(s)
Regalia, P.A. ; Dept. of Commun., Image, & Inf. processing, Inst. Nat. des Telecommun., Evry, France ; Kofidis, E.

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.

Published in:

Neural Networks, IEEE Transactions on  (Volume:14 ,  Issue: 4 )