Abstract
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.
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© 2007 Springer-Verlag Berlin Heidelberg
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Tichavský, P., Koldovský, Z., Oja, E. (2007). Speed and Accuracy Enhancement of Linear ICA Techniques Using Rational Nonlinear Functions. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds) Independent Component Analysis and Signal Separation. ICA 2007. Lecture Notes in Computer Science, vol 4666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74494-8_36
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DOI: https://doi.org/10.1007/978-3-540-74494-8_36
Publisher Name: Springer, Berlin, Heidelberg
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