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A new spike train metric

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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].

References

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    Victor JD, Purpura K: Nature and precision of temporal coding in visual cortex: A metric-space analysis. Journal of Neurophysiology. 1996, 76: 1310-1326.

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    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.

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    van Rossum MCW: A novel spike train distance. Neural Computation. 2001, 13: 751-763. 10.1162/089976601300014321.

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    Geisler WS, Albrecht DG, Salvi RJ, Saunders SS: Discrimination performance of single neurons: Rate and temporal information. Journal of Neurophysiology. 1991, 66: 334-362.

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    Rieke F, Warland D, de Ruyter van Steveninck R, Bialek W: Spikes: Exploring the neural code. 1997, Cambridge: MIT Press

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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).

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Correspondence to Cătălin V Rusu.

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Rusu, C.V., Florian, R.V. A new spike train metric. BMC Neurosci 11, P169 (2010) doi:10.1186/1471-2202-11-S1-P169

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Keywords

  • Topological Property
  • Spike Train
  • Actual Position
  • Hausdorff Distance
  • Mathematical Point