Independent Component Analysis without Preprocessing

Abstract

In this paper, we introduce a novel independent component analysis (ICA) algorithm, which does not require any preprocessing of the mixed signals (as opposed to most current ICA algorithms). Using a zero-forcing technique, the algorithm performs on-line diagonalization of a matrix whose entries are cross-cumulants of nonlinearly transformed mixtures of source signals. To our knowledge, the proposed approach is the only on-line ICA algorithm that separate mixed source signals without any frequently used preprocessing such as "centering" (subtracting the means from the mixtures) or "sphering" (decorrelation or whitening). Most other higher order cumulants based ICA algorithms involve complicated matrix algebra and lacks the desirable equivariant property which means these algorithms may fail to produce the desired source separation when the mixing matrix is ill-conditioned. The algorithm proposed in this paper, however, is equivariant and the separation performance of the algorithm is independent of the underlying mixing matrix.