Biomedical Engineering Reference
In-Depth Information
FIgURE 4.12:
An example of the outputs of two tracking systems, SYS1 (dashed line) and SYS2
(solid line), on top of actual hand trajectory (dotted line).
Selection of the Threshold.
The constraint on the
L
1
-norm of the LAR coefficients impacts the
neuronal subset selection as follows: a smaller threshold of the constraint will result in a large subset,
increasing a chance to select irrelevant channels, and a larger threshold will result in a smaller subset,
increasing a chance to miss relevant channels. Hence, a careful approach to determine this threshold
is critical. Towards this end, we propose using surrogate data to select the criterion parameters.
The surrogate data are generated to uncouple the hand movements from the neural activity
using two different procedures: 1) shifting either the kinematics or the neural activity, or 2) shuffling
the phase of the kinematic signals while preserving its power spectral density (PSD) to ensure the
same second-order statistics after perturbation [
32
]. The hypothesis is that there is no correlation
between the neural data and the hand movements in the surrogates. Therefore, the threshold should
be set such that no subsets are found in the surrogate data sets.
The online variable selection includes two components: a threshold for the correlation between
the model output
ˆ
LMS
and desired signal
d
(
n
); and a threshold for the maximum correlation in the
variable selection algorithm, that is
C
max
(
j
). The first threshold, δ
1
, plays a role such that the variable
selection algorithm is not activated when a correlation between
ˆ
d
( )
n
d
( )
n
LMS
and
d
(
n
) is lower than δ
1
. In
this case, no subset is selected at time
n
. This happens when the FIR filters are not sufficiently adapted
to track the target system. Accordingly, unreliable subsets may result if the selection is performed on
