Information Technology Reference
In-Depth Information
3.
Calculates the power spectrum for each component for all trials. The spectrum
length of each components is
L
s
where
L
s
= is the lowest power of 2 that is greater
than or equal to
L
. Let
S
i
denote the
N
L
s
power spectra matrix for trial
i
.
4.
Calculates
r
2
coefficients (coefficient of determination). This can be done inde-
pendently for each element of power spectra matrix. For a specific row and column
in power spectra matrix, let
x
1
and
x
2
be a set of elements of matrices
S
i
for all trials
i
that belong to classes 1 and 2, respectively. Let
n
1
and
n
2
be the number of trials
for classes 1 and 2, respectively. The values of
r
2
can be computed by the follow-
ing formula.
×
2
⎛
()
()
⎞
n
⋅
n
mean
x
−
mean
x
⎜
⎝
⎟
⎠
1
2
r
2
=
⋅
2
1
(9)
(
)
⎜
⎟
n
+
n
std
x
U
x
1
2
1
2
,
L
s
coefficient of determina-
tion matrix is denoted as
R
square
. Notice that only spectra samples in band pass fre-
quency range are calculated. For those whose frequency range is outside the band
pass range will not be considered and are set to be 0.
5.
Finds the value of
m
. We apply the maximum function to each row in
R
square
and
obtain vector
Rmax
. This vector is further divided into 2 halves:
Rmax
1
and
Rmax
2
.
Then, we try to locate the most stable spatial filter in each half. For the first half,
we locate the element index of
Rmax
1
that has the highest value of
r
2
. We also do
the same thing for second half. Let
imax
1
,
imax
2
denote these indices. Now we
want to find the set of prominent spatial filters which consists of the first and last
m
spatial filters of projection matrix
W
. The value of
m
is the larger of
imax
1
and (
N
-
imax
2
+1).
where
std
is the standard deviation. The resulting
N
×
3.2 Semi-automatic Selection Approach
1.
Follows the steps 1-4 of automatic selection approach described in section 3.1.
Also, obtains the vector
Rmax
1
and
Rmax
2
.
2.
Plots the values in
Rmax
1
and
Rmax
2
in separate graph. Sorts the values in descend-
ing order. The graphs should be arranged so that y-axis is
r
2
values and x-axis is
the element index of the vector.
3.
Manually locates the sharp drop. The last vector index before the drop is
idrop
1
for
the first graph and
idrop
2
for the second graph.
4.
Finds the maximum (minimum) index value from the portion of the sorted list
between the first and
idrop
1
(
idrop
2
). This value is
imax
1
(
imax
2
) in the first (sec-
ond) graph. The value of
m
can be derived in the same way as in the first approach.
3.3
A Working Example of Selection the Value of
m
For automatic selection method,
m
is obtained by comparing
imax
1
and
imax
2
which
are the element index of first bar of these 2 graphs. Thus
m
= max(1, 118 - 118 + 1)
= 1. For semi-automatic selection approach, sharp drops occur between the oblique
shaded and solid bars in figure 1. The left graph (sorted values of
Rmax
1
) shows that
idrop
1
is 2. In this case,
imax
1
happens to be the same as
idrop
1
. For the right graph
