A Variant of EFICA Algorithm with Adaptive Parametric Density Estimator

Abstract: FastICA is a popular method for Independent Component Analysis used for separation of linearly mixed independent sources. The separation proceeds through optimization of a contrast function that is based on kurtosis or other entropy approximations using a nonlinear function. The EFICA algorithm is a recently proposed version of this algorithm that is asymptotically efficient when all source distributions are from the Generalized Gaussian family. It is known that the optimal nonlinearity for entropy estimation is the score function of the source distribution. For its evaluation the knowledge of the probability density function (pdf) of the source signals is necessary. Because these pdfs are unknown, the EFICA algorithm assumes that the distribution is Generalized Gaussian Distribution, calculates its parameter α for each source and selects one nonlinearity from the available set for fine tuning of the sources. This paper proposes to modify the EFICA algorithm by parametric estimation of the real score function, which is subsequently used as the contrast function in fine tuning iterations. The algorithm is tested on artificial data; the results are compared to original EFICA, FastICA and JADE. I