Encyclopedia of Computational Neuroscience

Living Edition
| Editors: Dieter Jaeger, Ranu Jung

Metric Space Analysis of Neural Information Flow

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7320-6_744-1

In the metric-space approach to spike train analysis, spike trains are regarded as points in a metric space, that is, a space with a distance defined between any pair of points.

Spike Train Metrics

The Victor-Purpura metric (Victor and Purpura 1996) is one common way to define a metric distance between spike trains. The Victor-Purpura metric considers a fictional total cost for transforming one spike train into another using three basic operations: spike insertion, spike deletion and spike movement. Each basic operation is given an individual cost; one for inserting or deleting a spike and q| δt| for moving a spike a temporal distance δt. The cost-per-time, q, is a parameter, with the timescale 2/ q thought of as corresponding to the temporal precision of spike times in the metric. The distance between the two spike trains is then defined as the cost of the cheapest transformation of one to the other. In other words, the distance between spike trains x and y is given by
$$ d\left(x,\...

Keywords

Entropy Purpura 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of BristolBristolUK