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Soft dimension reduction for ICA by joint diagonalization on the Stiefel manifold.
In: Independent Component Analysis and Signal Separation. Berlin [u.a.]: Springer, 2009. 354-361 (Lecture Notes Comp. Sci. ; 5441)
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 $R^n$. 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.
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Publication type Article: Edited volume or book chapter
Editors Adali, T.*
Keywords independent component analysis (ICA); blind source separation (BSS); joint diagonalization; soft dimension reduction