A Projection Pursuit Methodology for Blind Signal Extraction

The current theory for Independent Component Analysis (ICA) tries to model the observations as unknown linear combination or mixture of N independent components or sources S1(t), . . . , SN(t) whose distribution is also usually unknown. In the ICA problem one tries to recover all the N independent and non-Gaussian components from the only knowledge of the observations. In this paper, we address the generalization of the problem where one tries to estimate with P ≤ N outputs Y1, . . . , YP (linear function of the observations) a subset of P of the N independent components. The paper presents, from an unified standpoint, several existing contrast for ICA (minimum mutual information, minimum entropy, maximum likelihood, negentropy, infomax, ...) but here considering the case of the extraction of a subset P of sources. This extension derives from the projection pursuit methodology presented in [1-4] and from the following related set of inequalities (where h(·) denotes differential entropy)