Volume 11 Supplement 1

Nineteenth Annual Computational Neuroscience Meeting: CNS*2010

Open Access

A new spike train metric

BMC Neuroscience201011(Suppl 1):P169

DOI: 10.1186/1471-2202-11-S1-P169

Published: 20 July 2010

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].

Declarations

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).

Authors’ Affiliations

(1)
Center for Cognitive and Neural Studies (Coneural), Romanian Institute of Science and Technology
(2)
Department of Computer Science, Babeş-Bolyai University

References

  1. Victor JD, Purpura K: Nature and precision of temporal coding in visual cortex: A metric-space analysis. Journal of Neurophysiology. 1996, 76: 1310-1326.PubMedGoogle Scholar
  2. Victor JD, Purpura K: Metric-space analysis of spike trains: Theory, algorithms and application. Network: Computation in Neural Systems. 1997, 8: 127-164. 10.1088/0954-898X/8/2/003.View ArticleGoogle Scholar
  3. van Rossum MCW: A novel spike train distance. Neural Computation. 2001, 13: 751-763. 10.1162/089976601300014321.View ArticlePubMedGoogle Scholar
  4. Geisler WS, Albrecht DG, Salvi RJ, Saunders SS: Discrimination performance of single neurons: Rate and temporal information. Journal of Neurophysiology. 1991, 66: 334-362.PubMedGoogle Scholar
  5. Rieke F, Warland D, de Ruyter van Steveninck R, Bialek W: Spikes: Exploring the neural code. 1997, Cambridge: MIT PressGoogle Scholar

Copyright

© Rusu and Florian; licensee BioMed Central Ltd. 2010

This article is published under license to BioMed Central Ltd.

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