A comparison of Euclidean metrics and their application in statistical inferences in the spike train space

TL;DR

This paper compares two Euclidean-like metrics for analyzing spike train data, demonstrating their theoretical properties, applications in statistical inference, and effectiveness in neural coding experiments.

Contribution

It provides a systematic comparison of two Euclidean-like metrics in spike train analysis and shows how both can be used for statistical inference in neural data.

Findings

Both metrics enable Euclidean embedding of spike train space.

Equivalent statistical inference methods are developed for both metrics.

Both frameworks perform well in neural coding applications.

Abstract

Statistical analysis and inferences on spike trains are one of the central topics in neural coding. It is of great interest to understand the underlying distribution and geometric structure of given spike train data. However, a fundamental obstacle is that the space of all spike trains is not an Euclidean space, and non-Euclidean metrics have been commonly used in the literature to characterize the variability and pattern in neural observations. Over the past few years, two Euclidean-like metrics were independently developed to measure distance in the spike train space. An important benefit of these metrics is that the spike train space will be suitable for embedding in Euclidean spaces due to their Euclidean properties. In this paper, we systematically compare these two metrics on theory, properties, and applications. Because of its Euclidean properties, one of these metrics has been further used in defining summary statistics (i.e. mean and variance) and conducting statistical inferences in the spike train space. Here we provide equivalent definitions using the other metric and show that consistent statistical inferences can be conducted. We then apply both inference frameworks in a neural coding problem for a recording in geniculate ganglion stimulated by different tastes. It is found that both frameworks achieve desirable results and provide useful new tools in statistical inferences in neural spike train space.