## Electronic Journal of Statistics

### Analysis of spike train data: Alignment and comparisons using the extended Fisher-Rao metric

#### 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.

#### Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 1776-1785.

Dates
First available in Project Euclid: 29 October 2014

https://projecteuclid.org/euclid.ejs/1414588162

Digital Object Identifier
doi:10.1214/14-EJS865B

Mathematical Reviews number (MathSciNet)
MR3273594

Zentralblatt MATH identifier
1305.62334

#### Citation

Wu, Wei; Srivastava, Anuj. Analysis of spike train data: Alignment and comparisons using the extended Fisher-Rao metric. Electron. J. Statist. 8 (2014), no. 2, 1776--1785. doi:10.1214/14-EJS865B. https://projecteuclid.org/euclid.ejs/1414588162

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