Imposing sparsity on the mixing matrix in independent component analysis

In independent component analysis, prior information on the distributions of the independent components is often used; some weak information may in fact be necessary for successful estimation. In contrast, prior information on the mixing matrix is usually not used. This is because it is considered that the estimation should be completely blind as to the form of the mixing matrix. Nevertheless, it could be possible to 1nd forms of prior information that are su2ciently general to be useful in a wide range of applications. In this paper, we argue that prior information on the sparsity of the mixing matrix could be a constraint general enough to merit attention. In a biological interpretation, sparseness of mixing matrix means sparse connectivity of the neural network. We show that the computational implementation of such sparsifying priors on the mixing matrix is very simple since in many cases they can be expressed as conjugate priors. The property of being conjugate priors means that essentially the same algorithm can be used as in ordinary ICA. c © 2002 Elsevier Science B.V. All rights reserved.