Mathematics in Independent Component Analysis

282 Chapter 20. Signal Processing 86(3):603-623, 2006
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Fig. 10. Mixing matrices recovered for the real s-EMG using different methods; (a)
JADE, (b, c) NMF with different preprocessing, (d, e) sparse NMF with the same
two preprocessing methods as NMF, and (f) SCA.
3.2 Real s-EMG signals
In this section we analyze real s-EMG recordings obtained from ten healthy
subjects. At first we will again study a single s-EMG and plot it for visual
inspection, and then show statistics over multiple subjects. The first data set
has been obtained from a single subject performing a sustained contraction at
30% MVC, see Fig. 9. The signal acquisition and preprocessing is described
in section 2.1.2.
We initially use JADE as ICA algorithm of choice. The estimated mixing
matrix is visualized in Fig. 10(a). As in the case of synthetic signals, we then
apply NMF and sparse NMF to both X+ and X∗ and obtain the recovered
mixing matrices visualized in Fig. 10(b-e).
We face the following problem when recovering the source signals by SCA.
If we use PCA to n = 3 dimensions, we cannot achieve convergence; also a
generalized Hough plot [37] does not reveal such structure. Hence we choose
dimension reduction to n = 2. In the two-dimensional projected mixtures, the
data clearly clusters along two lines, so the assumption of sparseness holds
in 2 dimensions. We use Mangasarian-style clustering / SCA (similar to kmeans)
[38] to recover these directions. The thus recovered mixing matrix in
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