An O(n) method of calculating Kendall correlations of spike trains

TL;DR

This paper introduces an O(n) algorithm for computing Kendall correlations of spike trains, significantly faster than existing methods, facilitating large-scale neural data analysis.

Contribution

The paper presents a novel linear-time algorithm for Kendall correlation of spike trains, improving computational efficiency in neuroscience data analysis.

Findings

The new algorithm is approximately 50 times faster than the standard O(n ln n) method.

Taking the specific nature of spike trains reduces runtime significantly.

A MATLAB implementation of the algorithm is publicly available.

Abstract

The ability to record from increasingly large numbers of neurons, and the increasing attention being paid to large scale neural network simulations, demands computationally fast algorithms to compute relevant statistical measures. We present an O(n) algorithm for calculating the Kendall correlation of spike trains, a correlation measure that is becoming especially recognized as an important tool in neuroscience. We show that our method is around 50 times faster than the O (n ln n) method which is a current standard for quickly computing the Kendall correlation. In addition to providing a faster algorithm, we emphasize the role that taking the specific nature of spike trains had on reducing the run time. We imagine that there are many other useful algorithms that can be even more significantly sped up when taking this into consideration. A MATLAB function executing the method described here has been made freely available on-line.