Biomedical Engineering Reference
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(a)
(b)
Fig. 8. Results on the plausible data set: (a) Riemannian Distance and (b) normalized Riemannian
Distance
Ta b l e 2 . Perfomance index (PI) values for plausible EEG: mean and standard deviation for the
four algorithms, with two initializations (whitening (W) and sphering (S)) and using the couple
n/N (nb. of channels / data length) given by the heuristic rule derived from figure 8(b).
n =8
n =16
n =24
n =32
n =48
N =2 × 512
N =3 × 512
N =4 × 512
N =5 × 512
N =7 × 512
W
S
W
S
W
S
W
S
W
S
FastICA
0.048 0.047 0.044 0.044 0.038 0.038 0.036 0.037 0.034 0.033
(0.014) (0.012) (0.007) (0.008) (0.006) (0.006) (0.004) (0.004) (0.004) (0.004)
AMICA
0.024 0.023 0.019 0.018 0.015 0.015 0.015 0.013 0.020 0.011
(0.012) (0.009) (0.004) (0.003) (0.001) (0.002) (0.008) (0.001) (0.021) (0.001)
Extended
0.159
0.089
0.207
0.097
0.218
0.085
0.162
0.055
0.173
0.058
Infomax
(0.099) (0.046) (0.061) (0.038) (0.038) (0.026) (0.024) (0.015) (0.017) (0.011)
JADER
0.040 0.040 0.039 0.039 0.036 0.036 0.037 0.037 0.123 0.123
(0.008) (0.008) (0.006) (0.006) (0.004) (0.004) (0.003) (0.003) (0.032) (0.032)
show to be very similar to the results obtained on the previous random data set. Thus,
plausible source time courses and mixture do not show to have high influence on these
second order statistics estimation, allowing to keep the same minimum data length rule
derived from figure 6(c). Table 2 gives mean PI related to this proposed decision rule
on the plausible data set, where it can be seen that these minimum data length bounds
appear to be adequate for all the algorithms in most channel size configurations, even
for Extended InfoMax when a sphering initialization is considered. Some lower per-
formances are observed for JADER for 48 channels, confirming the observation made
in the previous section that this decision rule might be inadequate for this method for
high number of channels. Relative better performances observed on Extended InfoMax,
and over all impressive results given by AMICA with sphering for channel size over 24
(mean PI < 0 . 015 with minimal standard deviation of 0 . 001 ) have to be explained in
the light of the initialization parameter.
Sphering Is Better Than Whitening for Dipolar Sources Separation. Figure 9 dis-
plays the evolution of PI with the data sample size for the five considered configura-
tions (channel number). A quick look at these curves let us conclude that FastICA and
 
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