Dimension reduction as a deflation method in ICA

Abstract

In independent component analysis (ICA), when using the one-unit contrast function optimization approach to estimate independent components one by one, the constraint of uncorrelatedness between independent components prevents the algorithm from converging to the previously found components. A popular way to achieve uncorrelatedness is the Gram-Schmidt-like decorrelation scheme. In fact, uncorrelatedness between independent components can be achieved by reducing the degree of freedom in the unknown parameter set of the de-mixing matrix. In this letter, we propose to exploit the dimension-reduction technique to exactly enforce uncorrelatedness between difference independent components. The advantage of this method is that dimension reduction of the observations and de-mixing weight vectors makes the computation complexity lower and produces a faster convergence. Hence, our method results in a faster algorithm in computation of ICA.