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

Abstract. 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 Rn . 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 trustregion 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.

• Type: Conference
• Year: 2009
• Where: IDA
• Authors: Fabian J. Theis, Thomas P. Cason, Pierre-Antoine Absil
• Keywords: Artificial Intelligence, Dimension Reduction, IDA 2009, Soft Dimension Reduction, Stiefel Manifold