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 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.
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Theis, F.J., Cason, T.P., Absil, P.A. (2009). Soft Dimension Reduction for ICA by Joint Diagonalization on the Stiefel Manifold. In: Adali, T., Jutten, C., Romano, J.M.T., Barros, A.K. (eds) Independent Component Analysis and Signal Separation. ICA 2009. Lecture Notes in Computer Science, vol 5441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00599-2_45
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DOI: https://doi.org/10.1007/978-3-642-00599-2_45
Publisher Name: Springer, Berlin, Heidelberg
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