Mathematics in Independent Component Analysis

1.6. Applications to biomedical data analysis 49
Component given by each method [a.u.]
(a) JADE
(b) NMF
(c) NMF*
(d) sNMF
(e) sNMF*
(f) SCA
(g) s-EMG
-2
-4
02468
-2
-4
02468
-2 02468
-2 0246
-2 02468
-2
-4
02468
0.5 1
1.5
-0.5 0
50 100 150 200 250 300 350 400 450 500
Time [ms]
Figure 1.27: A recovered sources after unmixing an sEMG data, (a-f) shows results obtained
using the different methods and (g) the original most-active sensor signal.
Our approach was therefore to apply and validate sparse BSS methods based on various
model assumptions to sEMG signals. When applied to artificial signals we found noticeable
differences of algorithm performance depending on the source assumptions. In particular, sparse
nonnegative matrix factorization outperforms the other methods with regards to increasing
additive noise. However, in the case of real sEMG signals we showed that despite the fundamental
differences in the various models, the methods yield rather similar results and can successfully
separate the source signal, see figure 1.27. This was due to the fact that the different sparseness
assumptions are only approximately fulfilled thus apparently forcing the algorithms to reach
similar results, but from different initial conditions using different optimization criteria.
The resulting sparse signal components can now be used for further analysis and for artifact
removal. A similar analysis using spectral correlations have been employed in (Böhm et al.,
2006, Stadlthanner et al., 2006b) to remove the water artifact from multidimensional proton
NMR spectra of biomolecules dissolved in aqueous solutions.