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

Authors:
Fabian J. Theis;Thomas P. Cason;P. -A. Absil
Affiliations:
CMB, Institute of Bioinformatics and Systems Biology, Helmholtz Zentrum München, MPI for Dynamics and Self-Organization, Göttingen, Germany;Department of Mathematical Engineering, Université catholique de Louvain, Louvain-la-Neuve, Belgium B-1348;Department of Mathematical Engineering, Université catholique de Louvain, Louvain-la-Neuve, Belgium B-1348
Venue:
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Year:
2009

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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 *** 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.