# Information Geometry as Applied to Neural Spike Data

**DOI:**https://doi.org/10.1007/978-1-4614-6675-8_395

## Definition

Information geometry studies invariant structures of a family of probability distributions. Such a family forms a Riemannian manifold together with a dual pair of affine connections (Amari and Nagaoka 2000). Neural spike train data are of stochastic nature described by probability distributions. Information geometry is applied for elucidating the properties of spiking processes spread over a number of neurons as well as over time.

## Detailed Description

Neuronal spike data are composed of a collection of binary variables *D* = {*x*_{i}(*t*)}, where *i* = 1, …, *n* denote the numbers of neurons in an ensemble and *t* denotes the discrete time, *t* = 1, 2, …, *T*, such that *x*_{i}(*t*) is 1 when a spike exists and 0 otherwise. The probability distribution governing {*x*_{i}(*t*)} is searched for from observed data in order to elucidate temporal and spatial correlations of spikes. Since *x*_{i}(*t*) are binary random variables, its distribution belongs to an exponential family, which is geometrically a dually flat...

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