Robust parallel fast-ICA algorithms using batch and adaptive MMSE estimators

Abstract

All the algorithms for ICA require high-order statistics to estimate the independent components. This is because second-order information is insufficient to assess that two random variables are independent of each other. It is known that the robustness of the high-order sample estimators is poor, meaning that a few outliers can change dramatically its value. In this paper, we generalize the alternative robust statistics for moments and cumulants introduced by Welling [1] presenting the MMSE-robust moments. Then we present a batch and adaptive versions of an algorithm for estimating the parameters that define the estimator. Finally, we modify two FastICA algorithms of ICA based on kurtosis and negentropy to apply the MMSE robust estimators and show some experiments with supergaussian sources to demonstrate the improvement.