Biomedical Engineering Reference
In-Depth Information
This property shows that the gamma filter decouples the memory depth from the filter or-
der by adjusting a feedback parameter (
μ
). In the case of
μ
= 1 (i.e., the FIR filter), the resolution
is maximized, whereas the memory depth is minimized for a given filter order. But this choice
sometimes results in overfitting when a signal to be modeled requires more time delays than the
number of descriptive parameters. Therefore, the gamma filter with the proper choice of a feedback
parameter can avoid overfitting by reducing the number of parameters required to span a certain
memory depth. Sandberg and Xu showed that the gamma neural model, which is obtained by
substituting the tap delay line in the TDNN by a gamma memory, is still a universal mapper in
functional spaces [
20
].
The tap weights can be either computed by LS or updated using NLMS, and therefore the
computational complexity is of the same order of FIR filters. The feedback parameter
μ
can also be
adapted from the data using an LMS type of update [
21
]. However, instead of adaptively finding
μ
,
we can search the best combination of
K
and
μ
through cross-validation.
In Table
4.2
, we can see that by using the Gamma architecture the number of model param-
eters can be reduced by 40%. The reduction yielded a 3% increase in the testing correlation coef-
ficient with a reduction in the variance.
4.1.3 Subspace Projection
In addition to unnecessary weights in the model, one of the challenges in the design of decoding
models for BMIs is that some neuron firings are not substantially modulated during task perfor-
mance, and they only add noise to the solution. In the overall representation contained within
these neural systems, the superfluous neurons may be coding other kinematics, sensory informa-
tion, or are involved in internal signaling within the network. Although these neurons are impor-
tant to the overall function of the network, they may not be correlated with the particular behavior
TaBlE 4.2
Comparison of testing performance and number of parameters
for the Gamma architecture and NLMS (1-sec memory depth)
NlMS
gaMMa
Testing correlation coefficient
for a reaching task
0.75 ± 0.20
0.78 ± 0.19
Number of parameters
2973
1191
