Biomedical Engineering Reference
In-Depth Information
After preprocessing the data, the kinematics model
F
can be estimated using the least
squares solution. A regularization factor should be used to compute the linear filter weights in the
tuning function (1e-4 in this analysis). It should also be noted that this Monte Carlo approach is
stochastic, that is, it introduces variation between realizations even with fixed parameters because of
the Poisson spike generation model. The most significant parameters include the kernel size
s
, the
number of particles
x
, and the intensity parameter
e
. For example, in the approximation of the
noise distribution
( )
x x
, the intensity param-
eter
e
or number of samples used to approximate the noise distribution can influence computational
time and performance of the approximation. The kernel size
s
is used to smooth the nonlinearity
in the tuning function and in this estimation of the nonlinear function
f
it was assigned 0.02.
This kernel size should be chosen carefully to avoid losing the characteristics of the tuning curve
and also to minimize noise in the curve.
Figure
6.12
shows one realization of the reconstructed kinematics from all 185 neurons for
1000 samples. The left and right column plots display respectively the reconstructed kinematics for
p
approximated by the histogram of
h
= -
k
k
k
k
-
1
Px
Py
desired
cc
exp
=0.81606
cc
MLE
=0.77496
desired
cc
exp
=0.87303
cc
MLE
=0.85
12
2
50
100
5
0
0
0
-50
-50
600
800
1000
1200
1400
1600
1800
600
800
1000
1200
1400
1600
1800
t
t
desired
cc
exp
=0.78555
cc
MLE
=0.77072
desired
cc
exp
=0.81325
cc
MLE
=0.7901
1
Vx
Vy
2
2
1
1
0
0
-1
-1
-2
-2
600
800
1000
1200
1400
1600
1800
600
800
1000
1200
1400
1600
1800
t
t
desired
cc
exp
=0.50655
cc
MLE
=0.47951
desired
cc
exp
=0.48513
cc
MLE
=0.4775
Ax
Ay
0.2
0.3
0.1
0.2
0
0.1
-0.1
0
-0.2
-0.1
600
800
1000
1200
1400
1600
1800
600
800
1000
1200
1400
1600
1800
t
t
FIgURE 6.12:
Reconstructed kinematics for a 2D reaching task.
