Biomedical Engineering Reference
In-Depth Information
overfi tting of the ICA model could occur and lead to distortions (Hyvärinen and
Oja
2000
). The most commonly used criterion for selecting the model order for ICA
is based on principal component analysis (PCA) of the data covariance matrix, in
which the model order is set as the number of eigenvalues that account for a certain
proportion of the total observed variance. For the fear recognition data, more than
75 % of the total variance can be explained by 20 ICs.
It is also useful, sometimes essential, to select a subset of ICs that are related to
brain activity. This can be executed manually (Onton and Makeig
2009
) or by using
automatic algorithms when characteristics of artifacts are known in prior, such as
ADJUST (Mognon et al.
2011
), which can be implemented using the EEGLAB
library (Delorme et al.
2011
).
ICA Algorithms
ICA can be classifi ed into two main categories according to the algorithmic
approach: one based on higher-order statistics (HOS) and another based on the
time structure [see review in (James and Hesse
2005
)]. HOS-based ICA seeks
statistical independence in sources, not through uncorrelatedness, as in PCA, but
through HOS, such as kurtosis and differential entropy. In contrast to HOS-based
ICA, in which temporal ordering of the signals is irrelevant, time-structure-based
ICA seeks independence in sources through temporal or spectro-temporal uncor-
relatedness. In comparison, HOS-based ICA seems less intuitive, as it discards the
temporal information of the data, which is apparently relevant in ECoG signals.
Moreover, time-structure-based ICA can be adapted to deal with nonstationary
signals (James and Hesse
2004
). However, HOS-based ICA is more effi cient com-
putationally and, thus, more practical when the number of channels and/or signal
length is large.
The three widely used HOS-based ICA algorithms are (1) FastICA, which aims
to maximize the magnitude of kurtosis to render the sources as independent as pos-
sible (Hyvärinen and Oja
1997
); (2) Infomax, a neural network gradient-based algo-
rithm that attempts to measure independence using differential entropy (Bell and
Sejnowski
1995
); and (3) JADE, a tensorial method that uses higher-order cumulant
tensors (Cardoso and Souloumiac
1993
). The three algorithms yield similar results
in the fear recognition data (not shown) and in fMRI data (Zibulevsky and
Pearlmutter
2001
); however, JADE possesses a limitation on high-dimensional data,
for numerical reasons. One straightforward approach that can be used for time-
structure-based ICA is based on spatio-temporal decorrelation, which maximizes
the independence between sources in the time domain (Ziehe and Müller
1998
;
Belouchrani et al.
1997
). This method is fl exible and more effective for the extrac-
tion of neurophysiologically meaningful components in short segment data, where
HOS-based ICA failed (James and Hesse
2004
), and can be implemented using
ICALAB toolboxes (Cichocki et al.
2002
). Another attractive approach that is par-
ticularly suitable for ECoG signals is based on spatio-spectro-temporal decorrela-
tion, which maximizes the independence between sources in both time and frequency
