Extraction of signals with higher order temporal structure using Correntropy

This paper addresses the problem of semi-blindly extracting one single desired signal using a priori information about its higher order temporal structure. Our approach is based on the maximization of the autocorrentropy function for a given time delay. The a priori information is quantified as a time delay and a size for a Gaussian kernel to set the free parameters in the correntropy function. Those values provide information which allows the proposed method to adapt a demixing vector to extract the desired signal without the indeterminacy of the permutation problem in blind source separation. Moreover, this method is different from those for Independent Component Analysis that separate all the available sources, which, in some problems, is not desirable or computationally possible. Since correntropy can be interpreted as a generalization of correlation, we demonstrate that it is a suitable measure for studying the temporal behavior of higher order statistics of a signal. Also, the flexibility brought by the kernel size selection allows the user to choose the range of statistics he is interested in. We show in simulations that correntropy achieve better or equal separation than other linear methods proposed in the literature for source extraction based on temporal structures.