A. Hyvärinen and E. Oja. A Fast Fixed-Point Algorithm for Independent Component Analysis.
Neural Computation, Vol. 9, No. 7, pp. 1483-1492, 1997.
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Abstract: We introduce a novel fast algorithm for Independent Component Analysis, which can be used for blind source separation and feature extraction. It is shown how a neural network learning rule can be transformed into a fixed-point iteration, which provides an algorithm that is very simple, does not depend on any user-defined parameters, and is fast to converge to the most accurate solution allowed by the data. The algorithm finds, one at a time, all non-Gaussian independent components, regardless of their probability distributions. The computations can be performed either in batch mode or in a semi-adaptive manner. The convergence of the algorithm is rigorously proven, and the convergence speed is shown to be cubic. Some comparisons to gradient based algorithms are made, showing that the new algorithm is usually 10 to 100 times faster, sometimes giving the solution in just a few iterations.