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performances on the training set (typically using cross-validation (Browne
2000
)) or multivariate mutual information measures, see, e.g., (Hall
2000
; Pudil
et al.
1994
; Peng et al.
2005
). This global measure of performance enables to
actually consider the impact of redundancies or complementarities between
features. Some measures also remove the need to manually select the value of
N
(the number of features to keep), the best value of
N
being the number
of features in the best subset identi
ed. However, evaluating the usefulness of
subsets of features leads to very high computational requirements. Indeed, there
are many more possible subsets of any size than individual features. As such
there are many more evaluations to perform. In fact, the number of possible
subsets to evaluate is very often far too high to actually perform all the evalu-
ations in practice. Consequently, multivariate methods usually rely on heuristics
or greedy solutions in order to reduce the number of subsets to evaluate. They
are therefore also suboptimal but usually give much better performances than
univariate methods in practice. On the other hand, if the initial number of
features is very high, multivariate methods may be too slow to use in practice.
7.3.2.2 Channel Selection
Rather than selecting features, one can also select channels and only use features
extracted from the selected channels. While both channel and feature selection
reduce the dimensionality, selecting channels instead of features has some addi-
tional advantages. In particular, using less channels means a faster setup time for the
EEG cap and also a lighter and more comfortable setup for the BCI user. It should
be noted, however, that with the development of dry EEG channels, selecting
channels may become less crucial. Indeed the setup time will not depend on the
number of channel used, and the BCI user will not have more gel in his/her hair if
more channels are used. With dry electrodes, using less channels will still be lighter
and more comfortable for the user though.
Algorithms for EEG channel selection are usually based or inspired from generic
feature selection algorithm. Several of them are actually analogous algorithms that
assess individual channel usefulness or subsets of channels discriminative power
instead of individual features or subset of features. As such, they also use similar
performance measures and have similar properties. Some other channel selection
algorithms are based on spatial
filter optimization (see below). Readers interested to
know more about EEG channel selection may refer to the following papers and
associated references (Schr
der et al.
2005
; Arvaneh et al.
2011
; Lal et al.
2004
;
Lan et al.
2007
), among many other.
ö
7.3.2.3 Spatial Filtering
Spatial
filtering consists in using a small number of new channels that are de
ned as
a linear combination of the original ones:
