Biomedical Engineering Reference
In-Depth Information
FIgURE 4.13:
Illustration of the maximum correlation in the online variable selection algorithm. Note
that
d
represents a desired output projected in the input space.
Therefore, the curve of
C
max
(
j
) over iterations can represent the correlation between each selected
input and a desired output.
4.3 EXPERIMENTal RESUlTS
We first determined two thresholds, δ
1
and δ
2
, by applying the linear adaptive systems to both the
original and surrogate data sets. The first surrogate data are composed of neuronal inputs and the
shifted HPs. The HP data are shifted by 5 sec for a hand reaching task because successive reaching
movements has an interval of approximately 10 sec. For the 2D cursor control task, the HP data are
shifted by 10 sec to sufficiently destroy synchronization. The second surrogate data consist of neu-
ronal inputs and the shuffled hand trajectory data in which the phase of the HP signals are shuffled
while preserving PSD.
Figure
4.14
shows an example of the curve of
C
max
(
j
) for the case when we use the original
data and the surrogate data, respectively. In this example,
C
max
(
j
) for both the original and the sur-
rogate data were evaluated at the same time instance. A large difference between the
C
max
curves
can be observed; for example, three channels were selected for the original data whereas only one
channel was selected for the surrogate data. The dotted line indicates the threshold of selection.
The linear adaptive systems were implemented for 2000-sec (20 000 samples three-dimensional
(3D) data and 1600-sec (16 000 samples) 2D data sets. The online variable selection algorithm starts
after 100 sec for the 3D data, and 400 sec for the 2D data, in order to allow the LMS to sufficiently
adapt filter weights in the beginning. A learning rate of LMS is set such that the sum of the FIR filter
outputs without subset selection can track the hand trajectory reasonably well in the original data.
Note that it must not be set too large, otherwise the filter weights change too rapidly over time, which
will lead to a large misadjustment; therefore, the estimation of the correlation of individual neuronal
channels from the filter outputs becomes unreliable.
