Method for analyzing spike patterns with Markov transition matrices and Kullback-Leibler divergence

Carl F Sabottke

doi:10.1186/1471-2202-14-s1-p340

Abstract

We describe a novel method for analyzing neural data that uses a combination of Markov transition matrices and Kullback-Leibler divergence to characterize spike history and spike patterns. For this method, the interspike intervals (ISIs) are divided into bins by quantiles, and a Markov transition matrix is computed for the ISI sequence. This Markov transition matrix is then compared to another Markov transition matrix constructed under the assumption of independent spiking. We then compute the Kullback-Leibler divergence between the distributions of ISI transition probabilities for each bin. The purpose of this method is to quantify the effects of spike history on neuron output and to help better characterize the flaws associated with assuming independent spiking. We test this method on both simulated data and experimental data from primary visual cortex of cats, publicly available through CRCNS [1-3]. Interspike intervals are simulated based on exponential and gamma distributions fit to the corresponding experimental ISI distributions.

Highlights

We describe a novel method for analyzing neural data that uses a combination of Markov transition matrices and Kullback-Leibler divergence to characterize spike history and spike patterns
We test this method on both simulated data and experimental data from primary visual cortex of cats, publicly available through CRCNS [1-3]
For spike time transitions after both the smallest and longest 10% of interspike intervals (ISIs) in the experimental data, the Kullback-Leibler divergence for these quantile groups is in many cases almost double the Kullback-Leibler divergence of the simulated data, and it can be more than an order of magnitude higher in some rarer cases

Summary

Introduction

We describe a novel method for analyzing neural data that uses a combination of Markov transition matrices and Kullback-Leibler divergence to characterize spike history and spike patterns. We test this method on both simulated data and experimental data from primary visual cortex of cats, publicly available through CRCNS [1-3].

Results

Conclusion