Abstract
We present a metric-based framework for analyzing statistical variability of the neural spike train data that was introduced in an earlier paper on this section [14]. Treating the smoothed spike trains as functional data, we apply the extended Fisher-Rao Riemannian metric, first introduced in Srivastava et al. [9], to perform: (1) pairwise alignment of spike functions, (2) averaging of multiple functions, and (3) alignment of spike functions to the mean. The last item results in separation phase and amplitude components from the functional data. Further, we utilize proper metrics on these components for classification of activities represented by spike trains. This approach is based on the square-root slope function (SRSF) representation of functions that transforms the Fisher-Rao metric into the standard $\mathbb{L}^{2}$ metric and, thus, simplifies computations. We compare our registration results with some current methods and demonstrate an application of our approach in neural decoding to infer motor behaviors.
Highlights
While introducing the spike train data being considered here, Wu et al [14] describe a need for phase-amplitude separation in functional data obtained by smoothing spike trains
We will apply a recently-developed method for function registration to analyze smoothed spike trains
As described in [14], the data is a set of spike trains in primate motor cortex recorded during four different movement patterns
Summary
While introducing the spike train data being considered here, Wu et al [14] describe a need for phase-amplitude separation in functional data obtained by smoothing spike trains. They argue that phase and amplitude components contain specific information about underlying neural signals, and one can facilitate decoding using metrics involving these two components individually. We will apply a recently-developed method for function registration to analyze smoothed spike trains. As described in [14], the data is a set of spike trains in primate motor cortex recorded during four different movement patterns.
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