Biomedical Engineering Reference
In-Depth Information
The size of the topology was chosen by experimentation: 3, 5, 15, and 30 PEs were chosen for
the hidden layer. Because we seek a model that accurately maps all novel neuronal firing patterns to
hand position, we must search for a network topology that minimizes the output bias and variance.
The operator must choose learning rates that slowly adjust the weights so that maximum infor-
mation is captured and the network does not simply track the trajectory. Overfitting the network
should also be avoided. The training should be stopped at the point of maximum generalization,
which is based on the minimum error produced by a validation set of data [
33
]. A plot of the CV
over epochs is presented in Figure
3.8
. For neuronal data, the early stopping method indicates that
training should be stopped at approximately 50 epochs of data. This method did not produce good
models. Research has verified CVs poor performance in some problems [
24
]. Other methods will
be presented later to quantify maximum generalization for neuronal modeling.
The testing outputs for the TDNN BMI are presented in Figure
3.9
. The TDNN performs
better than the linear filter in peak accuracy (CC = 0.77 ± 0.17) but suffers in smoothness. The
large number of free parameters in the TDNN is not only difficult to train but produce outputs
with large variances. The biggest difficulty with BMI models of this type is the enormous set of free
parameters produced by the large neural input vector (104 dimensions) and the multiplication by
the number of hidden PEs. Training the first layer of the TDNN with backpropagation is a difficult
task because of the attenuation of the error by the hidden layer PEs. Decreased input data dimen-
sionality will limit the number of free parameters in the adaptive system architecture. Simulations
express the need for preprocessing which prune neurons with the most information in the sparse
data set. This problem calls for an adaptive system with the nonlinear power of a TDNN but with a
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Time (100ms)
FIgURE 3.9:
Testing performance for a TDNN for a reaching task. Here, the red curves are the desired
x
,
y
, and
z
coordinates of the hand trajectory, whereas the blue curves are the model outputs.
