Biomedical Engineering Reference
In-Depth Information
99, 108, 110, 149, and 167 in the2D target hitting data were similarly observed in the top-ranked
sensitivity group. These comparisons show that neuronal subsets selected in our analysis significantly
contribute to building decoding models (nonlinear as well as linear models). The advantage of this
method would be the capability of detecting time-varying changes of composition of subsets.
To demonstrate the effect of the time-variant relationship between the neural activity and ki-
nematics to the decoding, we performed a brief statistical test on the decoding performance using the
linear filter. We first divided the entire data into three disjoint sequential segments, say, SEG1, SEG2,
and SEG3 (such that SEG1 preceded SEG2 and SEG3). Then, the first linear filter was built using
samples randomly drawn from SEG1, where the Wiener-Hopf solution was used to learn the filter
coefficients [
14
]. The second linear filter was built using samples randomly drawn from SEG2. After
building these filters, we drew samples randomly from the last segment SEG3, and used them to test
each filter's decoding accuracy. The accuracy was measured by the mean absolute error (MAE), which
indicates the mean distance between the actual hand trajectory and the estimated trajectory. We hy-
pothesized that the decoding accuracy of two filters should be similar to each other if the relationship
of neural activity to kinematics is unchanged. We repeated this building and decoding procedure mul-
tiple times, and obtained a set of MAE values for each filter. Then, a nonparametric statistical method
(the Kolmogorov-Smirnov (KS) test) was applied to test if two empirical distributions of the MAE
from each filter were statistically equal. Specifically, the null hypothesis of the KS test was given by,
,
(4.50)
H
:
F
(
e
)
³
F
(
e
)
0
1
2
where
F
i
(
|
e
|
) is an empirical cumulative density function (CDF) of the MAE from SEG1 (
i
= 1) or
SEG2 (
i
= 2). If
H
0
is rejected, the alternative hypothesis is then
F
1
(
|
e
|
) <
F
2
(
|
e
|
), which indicates
that the second linear filter yielded less errors.
The size of SEG1 or SEG2 was 800 sec long for the 3D data and 700 sec for the 2D data.
We randomly drew 4000 samples from each segment to build the linear filter. The size of SEG3
was 400 sec long for the 3D data and 200 sec for the 2D data. We randomly drew 500 samples from
SEG3 to test the linear filter. The procedure was repeated 1000 times. The empirical statistics are
described in Table
4.7
, in which it is clearly shown that the second linear filter decoded kinematics
TaBlE 4.7:
Average MAE using two linear filters (in centimeters)
3d
2d
First filter (SEG1)
32.83 ± 3.43
19.39 ± 0.47
Second filter (SEG2)
17.94 ± 0.61
18.64 ± 0.37
