Robust prewhitening for ICA by minimizing β-divergence and its application to FastICA

Many estimation methods for independent component analysis (ICA) requires prewhitening of observed signals. This paper proposes a new method of prewhitening named β-prewhitening by minimizing the empirical β-divergence over the space of all the Gaussian distributions. The value of the tuning parameter β plays the key role in the performance of our current proposal. An attempt is made to propose an adaptive selection procedure for the tuning parameter β for this algorithm. At last, a measure of performance index is proposed for assessing prewhitening procedures. Simulation results show that β-prewhitening efficiently improves the performance over the standard prewhitening when outliers exist; it keeps equal performance otherwise. Performance of the proposed method is compared with the standard prewhitening by both FastICA and our proposed performance index.