Biomedical Engineering Reference
In-Depth Information
correlation in least squares and for spike trains, but has this form because the binary nature of the
data. The parameter
α
is a regularizing parameter to properly condition the inverse.
This linear filter actually has a geometry interpretation. Figure
6.6
shows the first and the
second PCA components of the spike-triggered velocity vectors for neuron 72 (the blue plus symbol
in the figure). The velocity vectors for the same segment, which are represented by the green dots,
are also projected onto the same PCA component directions. If the neuron has tuning, we expect
that the first two components of spike-triggered velocity will be distributed differently from the
velocity vectors.
The optimal linear filter actually projects the multidimensional velocity vectors along the
direction where they differ the most from the spike-triggered velocity vectors.
For the time interval selected for the spike analysis (i.e., the time interval valid for a Pois-
son assumption in the collected data), a number is randomly drawn from a normalized uniform
distribution (i.e., 0 to 1) and compared with the instantaneous conditional firing probability. If the
neuron 72: time 3000-4000
2
real spikes
estimated firing probability
1.5
1
0.5
0
0
100
200
300
400
500
600
700
800
900
1000
time
one realization of spike generation
1
generated spikes
esuntated firing rate
0.8
0.6
0.4
0.2
0
0
100
200
300
400
500
600
700
800
900
1000
time
FIgURE 6.7:
Spike generation from the estimated tuning function for neuron 72.
