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operation), features for ERP are all linear and linear operations are commutative.
Since BCI classi
ers, e.g., LDA, are generally also linear, this means that the clas-
si
er could theoretically learn the spatial
filter as well. Indeed, both linearly com-
bining the original features
X
for spatial
filtering (
F
=
WX
), then linearly combining
y
¼
wF
¼
w
ð
WX
Þ¼
WX
the spatially
filtered signals for classi
cation (
) or directly
linearly combining the original features for classi
cation (
y
=
WX
) are overall a
simple linear operation. If enough training data are available, the classi
er, e.g., LDA,
would not need spatial
filtering. However, in practice, there is often little training data
available, and
first performing a spatial
filtering eases the subsequent task of the
classi
er by reducing the dimensionality of the problem. Altogether, this means that
with enough training data, spatial
filtering for ERP may not be necessary, and leaving
the classi
er learn everything would be more optimal. Otherwise, if few training data
are available, which is often the case in practice, then spatial
filtering can bene
t a lot
to ERP classi
cation (see also Rivet et al. (
2009
) for more discussion of this topic).
7.4.3 Summary of Signal-processing Tools for ERP-based BCI
In summary, when designing ERP-based BCI, it is important to use the temporal
information. This is mostly achieved by using the amplitude of preprocessed EEG
time points as features, with low-pass or band-pass
filtering and downsampling as
preprocessing. Feature selection algorithms can also prove useful. It is also
important to consider the spatial information. To do so, either using or selecting
relevant channels is useful. Using spatial
filtering algorithms such as xDAWN or
Fisher spatial
cient solution, particularly when little
training data are available. In the following, we will brie
filters can also prove a very ef
y describe some alter-
native signal-processing tools that are less used but can also prove useful
in
practice.
7.5
Alternative Methods
So far, this chapter has described the main tools used to recognize mental states in
EEG-based BCI. They are ef
cient and usually simple tools that have become part
of the standard toolbox of BCI designers. However, there are other signal-
processing tools, and in particular other kinds of features or information sources that
can be exploited to process EEG signals. Without being exhaustive, this section
brie
y presents some of these tools for interested readers, together with corre-
sponding references. The alternative EEG feature representations that can be used
include the following four categories:
Temporal representations: Temporal representations measure how the signal
varies with time. Contrary to basic features used for ERP, which simply consist
in the EEG time points over time, some measures have been developed in order
