Brain–Computer Interfaces - Index of

86 G. Pfurtscheller et al.
filters such as those generated by independent component analysis (ICA) or principal
component analysis (PCA). Simple spatial filters such as bipolar or Laplacian
derivations can also be applied. The method of common spatial patterns (CSP) [57]
is also widely used in the BCI community.
After this (optional) step, the most important descriptive properties of the signals
have to be determined – this is the goal of the subsequent feature extraction stage.
The goal of this stage is to maximize the discriminative information and therefore
to optimally prepare the data for the subsequent classification step.
Probably the most widely used features closely related to the concept of
ERD/ERS are those formed by calculating the power in specific frequency bands,
the so-called band power features. This is typically achieved by filtering the signals
with a band pass filter in the desired frequency band, squaring of the samples and
averaging over a time window to smooth the result. As a last step, the logarithm is
calculated in order to transform the distribution of this feature to a more Gaussianlike
shape, because many classifiers such as Fisher’s linear discriminant analysis
(LDA) in the next stage assume normally distributed features. Band power features
have been extensively used in the Graz BCI system. The initial band pass filter is
typically implemented with an infinite impulse response filter in order to minimize
the time lag between the input and output. The averaging block usually calculates
the mean power within the last second, which is most often implemented with a
moving average finite impulse response filter.
Other popular features also used by the Graz BCI are parameters derived from
an autoregressive (AR) model. This statistical model describes a time series (corresponding
to an EEG signal in the case of a BCI) by using past observations in order
to predict the current value. These AR parameters were found to provide suitable
features to describe EEG signals for subsequent classification in a BCI system and
can also be estimated in an adaptive way [61].
Both feature types mentioned above neglect the relationships between single
EEG channels. Such relations have proved to be useful in analyzing various neurophysiological
problems conducted in numerous studies (see [27, 34, 56, 63, 66]
for example) and could provide important information for BCIs. A specific coupling
feature, namely the phase synchronization value (or phase locking value), has
already been implemented and used in the Graz BCI system. It measures the stability
of the phase difference between two signals stemming from two electrodes
and could be a suitable measure to assess long-range synchrony in the brain [20].
In contrast to classical coherence, the signal amplitudes do not influence the result,
and thus this measure is thought to reflect true brain synchrony [66].
After the feature extraction stage, an important step in the signal processing chain
is determining which features contribute most to a good separation of the different
classes. An optimal way to find such an optimal feature set is to search in all possible
combinations, known as exhaustive search. However, since this method is too
time-consuming for even a small number of features, it cannot be used in practical
applications and therefore, suboptimal methods have to be applied.
A popular and particularly fast algorithm that yields good results is the so-called
sequential floating forward selection (SFFS) [55]. Another extremely fast feature