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Müller-Gerking et al. then applied CSP for feature extraction in BCI application [2].
Since some spatial filters from CSP projection matrix are useful than others, they
selected a subset of spatial filters consisting of the first and the last
m
spatial filters,
2
m
filters altogether. They claimed that the classification accuracy is insensitive to the
choice of
m
. The optimal value of
m
for their purpose was around 2 or 3. Much of the
later work in BCI followed their guideline and usually set
m
to be around 1-5. For
example,
m
was set to 3 in [3]; to 2 in [4], [5]; to 1 in [6]). In our previous work [7],
we found that this claim was not always valid and higher accuracy can be achieved
when setting the value of
m
to be greater than 5. Therefore, in this paper, we explore
the possibility to search for a reasonably good value of
m
in each individual classifi-
cation. We developed 2 selection approaches for finding this parameter: automatic
and semi-automatic selection approaches. The main idea is to sort spatial filters based
on their usefulness and identify the value of
m
based on the drop of usefulness of
spatial filters in this sorted order. Both selection approaches were assessed by using
the dataset 1 from BCI Competition IV [8, 9] and data IVa from BCI Competition III
[10]. The results show that our selection approaches usually provide a better value of
m
and the values are sometimes optimal.
This paper is organized as follows. Section 2 presents theoretical background of
CSP. Section 3 describes our selection approaches. Section 4 discusses the detail of
datasets used in our experiments. Section 5 provides the experimental results. Discus-
sion of results is presented in section 6 and the conclusion is given in section 7.
2 Theoretical Background on CSP and Analysis
In section 2.1, we provide an introduction to Common Spatial Patterns. We explain
our view of CSP and the idea that convinced us to design an approach to select a sub-
set of the spatial filters
in section 2.2.
2.1 Common Spatial Patterns (CSP)
CSP can be used as a feature extraction tool in two-class models. The main idea of
CSP is to find the projection matrix that maximizes variance for one class while
minimizes variance for the other class. Once data set is projected into this space, vari-
ance can be used as a feature in classification process.
Let
X
denote an
N
T
matrix of band passed and centered signal samples of a trial
where
N
is the number of channels and
T
is the number of samples. Centering can be
done for each channel individually by subtracting the mean amplitude of the particu-
lar channel from the signal amplitude for all samples in that channel. In order to use
CSP, several trials of both classes are needed.
The normalized spatial covariance of a trial
X
can be calculated as
×
T
XX
C
=
.
(1)
T
trace
(
XX
)
Let
C
avg
1
and
C
avg
2
denote the averages of covariance matrices of trials in classes 1
and 2 respectively, then
