Mathematics in Independent Component Analysis

284 Chapter 20. Signal Processing 86(3):603-623, 2006
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]
Fig. 12. One of the three recovered sources after applying A + to an s-EMG data
recorded at 30% MVC; (a-f) results obtained using the different methods; (g) original
source signal.
In order to be able to draw statistically more relevant conclusions, we compare
the various BSS algorithms for s-EMGs of nine subject, recorded at 30% MVC.
Fig. 12 plots a single extracted source for each BSS algorithms; Fig. 12(g)
shows the s-EMG channel where the dominant source signal is chosen for
comparison. One problem of performing batch comparisons however lies in the
fact that separation performance is commonly evaluated by visual inspection
or at most by comparison with other separation methods — because of course
the original sources are unknown. We cannot do plots similar to Fig. 12 for
each subject, so in order to provide a more objective measure, we consider the
main application of BSS for real s-EMG analysis — preprocessing in order to
achieve ‘cleaner’ data for template matching.
A common measure for this is to count the number of zero-crossings of the
sources (after combining them to a full eight dimensional observation vector by
taking only the maximally active source in each channel). Note that this zerocrossing
count is already outputted by the MDZ filter. It is directly related
to the amount of MUAPs present in a s-EMG signal [46], and by comparing
this index before and after the BSS algorithms, we can analyze whether and
to what extent they actually enhance the signal. With the aid of the MDZ
filter, we count the number of waves (the excursion of the signal between two
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