Dimension Reduction Based on Orthogonality —a Decorrelation Method in ICA

Abstract. In independent component analysis problems, when we use a one-unit objective function to iteratively estimate several independent components, the uncorrelatedness between the independent components prevents them from converging to the same optimum. A simple and popular way of achieving decorrelation between recovered independent components is a deflation scheme based on a Gram-Schmidt-like decorrelation [7]. In this method, after each iteration in estimation of the current independent component, we subtract its ‘projections ’ on previous obtained independent components from it and renormalize the result. Alternatively, we can use the constraints of uncorrelatedness between independent components to reduce the number of unknown parameters of the de-mixing matrix directly. In this paper, we propose to reduce the dimension of the de-mixing matrix to decorrelate different independent components. The advantage of this method is that the dimension reduction of the observations and de-mixing weight vectors makes the computation lower and produces a faster and efficient convergence.