Mathematics in Independent Component Analysis

Chapter 20. Signal Processing 86(3):603-623, 2006 285
subject ID JADE NMF NMF∗ sNMF sNMF∗ SCA
b 9% 7% 9% 10% 11% 10%
f 5% 3% 5% 4% 5% 4%
g 37% 35% 35% 35% 36% 30%
k 35% 35% 35% 35% 34% 38%
m 16% 16% 17% 16% 16% 13%
og 9% 8% 8% 8% 8% 10%
ok 3% 7% 9% 9% 10% 7%
s 41% 42% 42% 41% 41% 37%
y 71% 71% 73% 71% 73% 74%
means 25.0 % 25.1 % 25.7% 25.4% 25.8 % 24.6 %
std. deviations 21.4 % 21.4 % 21.3% 20.9% 21.0% 21.4 %
Table 4
Negative zero-crossing mean ratios i.e. relative enhancements for each subject, together
with mean performance of each algorithm.
consecutive zero crossings) and take the mean over all channels before and
after applying each of the BSS algorithms. We then subtract the latter from
the previous value and divide by the initial number of waves in order to have
an index than can be compared between different signals. Tab. 4 shows the
resulting ratios for the nine subjects. All BSS algorithms result in a reduction
of zero-crossings, and best results per run are achieved by NMF∗, sNMF∗ and
SCA. We see that in the mean, all algorithm perform somewhat similarly,
with sNMF∗ being best and SCA being worst. Hence the best algorithm for
this data set, sNMF∗, achieved a mean reduction of the number of waves
was 25.8%, which means that after applying the algorithms each channel is
composed, in average, of one fourth of the original number of waves, making
the template-matching technique easily applicable.
4 Discussion
The main focus of this work lies in the application of three different sparse
BSS models — source independence, (sparse) nonnegativity and k-sparseness
— to the analysis of s-EMG signals. This application is motivated by the fact
that the underlying MUAPTs exhibit properties (mainly sparseness) that fit
quite well to the three in principle different models. Furthermore, we take
interest in how well these models behave in the case of slightly perturbed
initial conditions — ICA for instance is known to be quite robust against
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