Applying ICA in EEG: Choice of the Window Length and of the Decorrelation Method - Biomedical Engineering Systems and Technologies - page 260

In this particular case of dipolar mixing, the reasons of the superiority of sphering
over whitening can be found in [5]: The objective of Principal Component Analysis
(PCA) 4 is to lump together as much variance as possible into each successive principal
component, whose scalp maps must then be orthogonal to all the others and therefore
are not free to model a scalp source projection resembling a single dipole. In other
words, whitening initialize the algorithm far from the solution, leading to a more diffi-
cult convergence for methods based on natural gradient descent like Extended InfoMax
and AMICA. On the other hand, Delorme et al. [5] emphasize that: Sphering com-
ponents, in particular, most often have stereotyped scalp maps consisting of a focal
projection peaking at each respective data channel and thus resembling the projection
of a radial equivalent dipole. . Consequently, sphering leads to initialization point much
more closer to the solution than whitening in the dipolar case, as it is confirmed and
quantified by our results.

6 Conclusions and Future Work

The first goal of this paper was to define a low bound of data length for robust sepa-
ration results. Four ICA algorithms often used to analyse EEG signals were tested on
different data lengths ( 1 to 20 seconds at 512 Hz sampling rate) and number of signals
( 8 , 16 , 24 , 32 and 48 sources/channels). A rule of minimum sample size is derived from
separation results on a random data set consisting of subgaussian and supergaussian
source signals mixed by random mixing matrices, and is validated on a plausible data
set in which sources were simulated by a macroscopic model of neuronal population
and mixed by dipolar mixing matrices obtained from a three layers head model. This
low bound is based on an original, normalized distance measure inspired by the com-
puter vision community and leads to a reasonable minimum time length. According to
our results (Tables 1 and 2), the proposed minimal data length rule guarantees a good
source separation performance with performance indexes ( PI ) under 0 . 05 in most con-
figurations for FastICA, JADER and AMICA (at least in the plausible case). Extended
InfoMax has to be considered separately, as this algorithm requires much more data
points. Our decision rule gives minimum data length much smaller than those recom-
mended in literature (over 5 n 2 ) for high number of channels n , being thus more in
adequation with the short time stationarity hypothesis accepted for EEG signals and
needed for most ICA algorithms.
A second objective was to evaluate the impact of initialization on the separation per-
formances using whitening or sphering in the first step of these algorithms. Due to the
optimization strategy on which they are based, FastICA and JADER show no sensitiv-
ity to initialization (decorrelation method). Conversely, natural gradient descent based
algorithms AMICA and Extended-Infomax show high sensitivity to initialization. Due
to their optimization strategy, these algorithms are much more time consuming and less
robust facing outliers, thus requesting an adequate initialization for a reliable conver-
gence with acceptable number of iterations. In the particular case of EEG, modelled as
a mixture of dipolar sources, it is possible to initialize the algorithm “near” the solution
by sphering. Consequently, the performances of these algorithms improve and they can

4

Equivalent to whitening.