Biomedical Engineering Reference
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(a)
(b)
(c)
Fig. 6. Results on the random data set: (a) Riemannian Distance, (b) normalized Riemannian
Distance and (c) Minimum length rules from literature vs proposed (linear) rule
over whitening initialization in the context of dipolar sources separation. For each data
set, the four algorithms are evaluated on 8 , 16 , 24 , 32 and 48 source sizes with sample
size varying from 1s to 20s with a 1s step (at a 512 Hz sampling rate). The number of
iteration for each source size/sample size has been set to 50 , a new set of data (random
data sources, plausible data sources, mixing matrices) being simulated at each iteration.
5.1
Random Data Set
A Minimum Length Rule. This section presents the results of the covariance esti-
mation accuracy vs the length of the data. In a previous work [16], the distance be-
tween covariance matrices was computed using (4) from different sample sizes starting
from 100 till 5000 by 100 points step, and number of channels taking values in the
set
. The likelihood was further evaluated using (11). A constant
threshold was empirically fixed to p =0 . 95 (Figure 6(a)): likelihood values above
this threshold was assumed to guarantee good estimation of covariances as stated in
section 3.1. However, this previous study already outlined that this rule might be too
strong, leading in a ever decreasing PI with the number of channels. This obser-
vation has been confirmed when studying this evolution of PI on larger number of
channels. Therefore,we proposed the normalized Riemannian distance defined by (10)
with the objective to refine our minimum length rule. Again, likelihood values above a
threshold of 0 . 95 were assumed to guarantee good estimation of second order statistics
{
8 , 10 , 12 , 14 , 16 , 18
}
 
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