Mathematics in Independent Component Analysis

Chapter 20. Signal Processing 86(3):603-623, 2006 283
1.5
1
0.5
0
SCA
sNMF *
sNMF
NMF *
NMF
sNMF *
sNMF
NMF *
NMF
JADE
(a) matrix comparison by Amari index
Measure value [a.u.]
2.5
2
1.5
1
0.5
0
KLD
MuIn
QMI
RSD
Renyi
Measure STW
Xcor
JADE
SCA NMFNMF sNMF
*
sNMF Channels
*
Signal
(b) comparison of the recovered sources
Fig. 11. Inter-component performance index comparisons; (a) comparison of the
Amari index; (b) mean of various source dependence measures.
JADE NMF NMF∗ sNMF sNMF∗ SCA
mean kurtosis 4.97 4.74 4.80 4.81 4.80 4.82
sparseness 0.387 0.424 0.413 0.408 0.407 0.405
σ(A✷) 0.76 0.50 0.55 0.60 0.62 0.70
Table 3
Comparison of sparseness of the recovered sources (real s-EMG data).
two dimensions is plotted in Fig. 10(f). Note that the SCA matrix columns
match two columns of the mixing matrices found by the other methods.
Similar to the toy data set, we compare the recoveries based on the different
methods using various indices from section 2.3 for mixing matrices and recovered
sources , Fig. 11. In contrast to the artificial signals, here all methods
yield rather similar performance, the mean Amari indices are roughly half the
value of the indices in the toy data setting. This confirms that the methods
recover rather similar sources.
As in the case of artificial signals, we again compare the sparseness of the
recovered sources, see Tab. 3. Due to the noise present in the real data, the
signals are clearly less sparse than the artificial data. Furthermore a comparison
between the various methods yields noticeably less differences than in
the case of artificial signals. At first glance it seems unclear why SCA performs
worse in terms of k-sparseness (using σ(A)) than the NMF methods,
but better than JADE. This however can be explained by the fact that the
PCA dimension reduction reduces the number of parameters hence SCA cannot
search the whole space, so it performs worse than NMF in that respect.
However it outperforms JADE, which also uses PCA preprocessing.
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