Biomedical Engineering Reference
In-Depth Information
Figure continued
3.2 NoNlINEaR ModElS
3.2.1 Time delay Neural Networks
The primary assumption in the Wiener filter topology is that the input output map is linear,
which may not be the case for the neural representation of movement control. To move beyond this
assumption for biological systems, dynamic neural networks (a time delay neural network or recur-
rent neural networks [
11
,
12
,
19
,
25
,
34
,
35
]) can be utilized to enhance the simple linear solution
at the expense of more sophisticated topologies and training algorithms. In time series analysis,
static nonlinear architectures such as the multilayer perceptron (MLP) or the radial basis function
network cannot be utilized. Indeed, the hallmark of time series is that there are dependencies hid-
den in the time structure of the signal, and this holds true for the dynamics of neuronal modulation.
Therefore, instantaneous mappers will not capture these dependencies over the lags. Spatiotemporal
nonlinear mappings of neuronal firing patterns to hand position can be constructed using an input
based time-delay neural networks (TDNNs) [
23
]. The input based TDNN is an MLP preceded
by a delay line that feeds each processing element (PE) of the hidden MLP layer with a vector of
present and past input samples. Normally, the nonlinearity is of the sigmoid type (either a logistic
