Speed and accuracy enhancement of linear ICA techniques using rational nonlinear functions

Authors:
Petr Tichavský;Zbyněk Koldovsky;Erkki Oja
Affiliations:
Institute of Information Theory and Automation, Praha 8, Czech Republic;Institute of Information Theory and Automation, Praha 8, Czech Republic and Faculty of Mechatronic and Interdisciplinary Studies, Technical University of Liberec, Liberec, Czech Republic;Adaptive Informatics Research Centre, Helsinki University of Technology, HUT, Finland
Venue:
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Year:
2007

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Abstract

Many linear ICA techniques are based on minimizing a non-linear 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.