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Speed and accuracy enhancement of linear ICA techniques using rational nonlinear functions. (English) Zbl 1172.94493

Davies, Mike E. (ed.) et al., Independent component analysis and signal separation. 7th international conference, ICA 2007, London, UK, September 9–12, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-74493-1/pbk). Lecture Notes in Computer Science 4666, 285-292 (2007).
Summary: Many linear ICA techniques are based on minimizing a nonlinear contrast function and many of them use a hyperbolic tangent (tanh) as their built-in nonlinearity. In this paper we propose two rational functions to replace the tanh and other popular functions that are tailored for separating supergaussian (long-tailed) sources. The advantage of the rational function is two-fold. First, the rational function requires a significantly lower computational complexity than tanh, e.g. nine times lower. As a result, algorithms using the rational functions are typically twice faster than algorithms with tanh. Second, it can be shown that a suitable selection of the rational function allows to achieve a better performance of the separation in certain scenarios. This improvement might be systematic, if the rational nonlinearities are selected adaptively to data.
For the entire collection see [Zbl 1129.94002].

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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