Biomedical Engineering Reference
In-Depth Information
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FIgURE 4.10:
An illustration of the LAR procedure.
joint set. The LAR procedure can be continued with the remaining inputs because they still have
the same absolute correlation with the current residual.
There are three major considerations in the implementation of LAR. First, LAR assumes
the linearly independence between input variables. Second, the determination of threshold for the
L
1
norm of coefficients is an open data-dependent problem. The performance of the linear model
learned by LAR can be greatly influenced by a choice of this threshold. Finally, LAR was originally
derived for static data. If we attempt to apply LAR to a linear model in BMIs, we have to cope
with these three difficulties. Indeed, the embedded inputs are likely to be correlated with each other
(although they might be linearly independent), so that LAR might not be able to operate optimally.
Also, finding an optimal threshold will be a nontrivial task, but we may devise a surrogate data
method to deal with this difficulty. The third issue is critical because the procedure has to be applied
online for channel selection, and we will start by addressing our implementation [
6
] that can have
wide applicability to time series modeling (not only BMIs).
online Variable Selection.
The LAR algorithm has been applied to variable selection in multi-
variate data analysis (static problems), but because LAR selects input variables by computation of
correlation using the entire data set, it requires the assumption of stationary statistics when applied
to time series. Therefore, a modified version of LAR, which selects a subset of input variables lo-
cally in time without the stationary assumption, has been proposed in Kim et al. [
6
]. Moreover, this
algorithm provided can be computed online, and provides a real-time variable selection tool for the
time-variant system identification problems.
Correlation between neuronal inputs and the desired response (hand trajectory) can be ac-
complished by recursively updating the correlation vector. The input covariance matrix can also be
