Fast equivariant JADE

Independent component analysis (ICA) is a widely used signal processing tool having applications in various fields of science. In this paper we focus on affine equivariant ICA methods. Two such well-established estimation methods, FOBI and JADE, diagonalize certain fourth order cumulant matrices to extract the independent components. FOBI uses one cumulant matrix only, and is therefore computationally very fast. However, it is not able to separate identically distributed components which is a major drawback. JADE overcomes this restriction. Unfortunately, JADE uses a huge number of cumulant matrices and is computationally very heavy in high-dimensional cases. In this paper, we hybridize these two methods. The affine equivariant FOBI estimate is used as an initial value for JADE, and only a small subset of most informative cumulant matrices is then diagonalized. In simulation studies we show that the new affine equivariant estimate is almost as good as JADE, and it is computationally much faster.