Soft Dimension Reduction for ICA by Joint Diagonalization on the Stiefel Manifold

Joint diagonalization for ICA is often performed on the orthogonal group after a pre-whitening step. Here we assume that we only want to extract a few sources after pre-whitening, and hence work on the Stiefel manifold of p -frames in *** n . The resulting method does not only use second-order statistics to estimate the dimension reduction and is therefore denoted as soft dimension reduction. We employ a trust-region method for minimizing the cost function on the Stiefel manifold. Applications to a toy example and functional MRI data show a higher numerical efficiency, especially when p is much smaller than n , and more robust performance in the presence of strong noise than methods based on pre-whitening.