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Fig. 7.4 Left channels used in bipolar spatial filtering over channels C3 and C4. Right channels
used in Laplacian spatial filtering over channels C3 and C4
number of source signals obtained with inverse solutions is often larger than the
initial number of channels, it is necessary to use feature selection or dimensionality
reduction algorithms.
The second category of spatial
filters, is optimized
for each subject according to training data. As any data-driven algorithm, the spatial
filters, i.e., data-driven spatial
filter weights w i can be estimated in an unsupervised way, that is without the
knowledge of which training data belong to which class, or in a supervised way,
with each training data being labeled with its class. Among the unsupervised spatial
filters, we can mention principal component analysis (PCA), which
finds the spatial
filters that explain most of the variance of the data, or independent component
analysis (ICA), which
filters whose resulting signals are independent
from each other (Kachenoura et al. 2008 ). The later has been shown rather useful to
design spatial
find spatial
filters able to remove or attenuate the effect of artifacts (EOG, EMG,
etc. (Fatourechi et al. 2007 )) on EEG signals (Tangermann et al. 2009 ; Xu et al.
2004 ; Kachenoura et al. 2008 ; Brunner et al. 2007 ). Alternatively, spatial
filters can
be optimized in a supervised way, i.e., the weights will be de
ned in order to
optimize some measure of classi
cation performance. For BCI based on oscillatory
EEG activity, such a spatial
filter has been designed: the common spatial patterns
(CSP) algorithm (Ramoser et al. 2000 ; Blankertz et al. 2008b ). This algorithm has
greatly contributed to the increase of performances of this kind of BCI and thus has
become a standard tool in the repertoire of oscillatory activity-based BCI designers.
It is described in more details in the following section, together with some of its
variants.
7.3.3 Common Spatial Patterns and Variants
Informally, the CSP algorithm
finds spatial
filters w such that the variance of the
filtered signal is maximal for one class and minimal for the other class. Since the
 
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