This article is part of the supplement: Nineteenth Annual Computational Neuroscience Meeting: CNS*2010

Poster Presentation

A new spike train metric

Cătălin V Rusu^1,2* and Răzvan V Florian¹

• * Corresponding author: Cătălin V Rusu rusu@coneural.org

Author Affiliations

¹ Center for Cognitive and Neural Studies (Coneural), Romanian Institute of Science and Technology, Cluj-Napoca 400487, Romania

² Department of Computer Science, Babeş-Bolyai University, Cluj-Napoca 400084, Romania

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BMC Neuroscience 2010, 11(Suppl 1):P169 doi:10.1186/1471-2202-11-S1-P169

The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2202/11/S1/P169

Published:

20 July 2010

© 2010 Rusu and Florian; licensee BioMed Central Ltd.

Poster Presentation

The theoretical and practical importance of quantifying the degree of similarity between pairs of spike trains has resulted in a plethora of spike train metrics. Some are based on cost functions [1,2] while others use smoothing kernels [3] or binning techniques [4] and then rely on spike intervals or precise spike timings to compute the distance. Spike metrics are especially important as they enable the analysis of the neural code, a fundamental and heavily debated issue in neuroscience. Here, we introduce a new class of spike train metrics dependent on smooth kernels. They compute the distance between pairs of spike trains and yield a result that is non-linearly dependent on the precise timing of the differences across the two spike trains. In this situation, the actual position of a spike outweighs the importance of the inter-spike interval. In the exchange of information between two neurons each spike may be as important as the spike train itself [5] and therefore, metrics based on the specific timing of differences are desirable.

The introduced spike train metrics, which will be referred to as max-metrics, are similar to the Hausdorff distance between two non-empty compact sets. They are given in two distinct forms: one that uses a convolution kernel to filter each spike train and, the other that uses the raw spike times. Because the latter does not rely on a smoothing kernel and uses the spike train directly, it does not introduce additional time constants and therefore has the advantage that it is more general. From a mathematical point of view the kernels can be just about any function because the generated metrics are commensurable. Some, however, will have a lesser physiological interpretation than others. The space of spike trains endowed with either form of the max-metric is compact. The implication for learning is that any learning rule based on the metric will eventually converge to a point in the spike train space. Because the max-metric generates the same topology regardless of the choice of kernels, topological properties such as compactness are common to all spike train spaces. The metrics are benchmarked against a simple spike count distance and against the original and a modified version of the van Rossum metric [3].

Acknowledgements

Supported by The Sectorial Operational Programme Human Resources Development (Contract POSDRU 6/1.5/S/3) and a grant of the Romanian National Authority for Scientific Research (PNCDI II, Parteneriate, contract no. 11-039/2007).

References