Journal of Computational Neuroscience

, Volume 30, Issue 1, pp 201–209 | Cite as

A metric space approach to the information channel capacity of spike trains



A novel method is presented for calculating the information channel capacity of spike trains. This method works by fitting a χ-distribution to the distribution of distances between responses to the same stimulus: the χ-distribution is the length distribution for a vector of Gaussian variables. The dimension of this vector defines an effective dimension for the noise and by rephrasing the problem in terms of distance based quantities, this allows the channel capacity to be calculated. As an example, the capacity is calculated for a data set recorded from auditory neurons in zebra finch.


Spike train Information channel capacity Gaussian channel χ-distribution Metric space van Rossum metric 



JBG wishes to thanks the Irish Research Council of Science, Engineering and Technology for an Embark Postgraduate Research Scholarship. CJH wishes to thank Science Foundation Ireland for Research Frontiers Programme grant 08/RFP/MTH1280. They are grateful to Garrett Greene, Louis Aslett and Daniel McNamee for useful discussion and to Kamal Sen for the use of the data analysed here.


  1. Anderson, T. W., & Darling, D. A. (1952). Asymptotic theory of certain ‘goodness-of-fit’ criteria based on stochastic processes. Annals of Mathematical Statistics, 23, 193–212.CrossRefGoogle Scholar
  2. Bialek, W., Rieke, F., de Ruyter van Steveninck, R. R., & Warland, D. (1991). Reading a neural code. Science, 252, 1854–1857.CrossRefPubMedGoogle Scholar
  3. Borst, A., & Theunissen, F. (1999). Information theory and neural coding. Nature Neuroscience, 2, 947–957.CrossRefPubMedGoogle Scholar
  4. Cover, T. M., & Thomas J. A. (1991). Elements of information theory. Wiley.Google Scholar
  5. De Ruyter Van Steveninck, R. R., Lewen, G. D., Strong, S. P., Koberle, R., & Bialek, W. (1997). Reproducibility and variability in neural spike trains. Science, 275, 1805–1808.CrossRefPubMedGoogle Scholar
  6. Dubbs, A. J., Seiler, B. A., & Magnasco, M. O. (2009). A fast \(\mathcal{L}_p\) spike alignment metric. arxiv/0907.3137.
  7. Houghton, C. (2009a). A comment on ‘a fast l_p spike alignment metric’ by A. J. Dubbs, B. A. Seiler, & M. O. Magnasco. arxiv:0907.3137, arxiv/0908.1260.
  8. Houghton, C. (2009b). Studying spike trains using a van Rossum metric with a synapses-like filter. Journal of Computational Neuroscience, 26, 149–155.CrossRefPubMedGoogle Scholar
  9. Houghton, C., & Victor, J. (2010). Measuring representational distances—The spike-train metrics approach. In N. Kriegeskorte, G. Kreiman (Eds.), Understanding visual population codes – toward a common multivariate framework for cell recording and functional imaging. MIT Press (in press).Google Scholar
  10. Johnson, D. H. (2003). Dialogue concerning neural coding and information theory.
  11. Narayan, R., Graña, G., & Sen, K. (2006). Distinct time scales in cortical discrimination of natural sounds in songbirds. Journal of Neurophysiology, 96, 252–258.CrossRefPubMedGoogle Scholar
  12. Rieke, F., Warland, D., De Ruyter Van Steveninck, R. R., & Bialek, W. (1999). Spikes: Exploring the neural code. MIT Computational Neuroscience Series.Google Scholar
  13. Rubin, I. (1974a). Information rates and data-compression schemes for Poisson processes. IEEE Transactions on Information Theory, 20, 200–210.CrossRefGoogle Scholar
  14. Rubin, I. (1974b). Rate distortion functions for non-homogeneous Poisson processes. IEEE Transactions on Information Theory, 20, 669–672.CrossRefGoogle Scholar
  15. Shannon, C. E. (1948). A mathematical theory of communication. Bell Systems Technical Journal, 27, 379–423, 623–656.Google Scholar
  16. Silverman, B. W. (1986). Density estimation. London: Chapman and Hall.Google Scholar
  17. Stephens, M. A. (1974). EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69, 730–737.CrossRefGoogle Scholar
  18. van Rossum, M. (2001). A novel spike distance. Neural Computation, 13, 751–763.CrossRefPubMedGoogle Scholar
  19. Victor, J. D. (2002). Binless strategies for estimation of information from neural data. Physical Review E, 66, 051903.CrossRefGoogle Scholar
  20. Victor, J. D. (2005). Spike train metrics. Current Opinion in Neurobiology, 15, 585–592.CrossRefPubMedGoogle Scholar
  21. Victor, J. D., & Purpura, K. P. (1996). Nature and precision of temporal coding in visual cortex: A metric-space analysis. Journal of Neurophysiology, 76, 1310–1326.PubMedGoogle Scholar
  22. Wang, L., Narayan, R., Graña, G., Shamir, M., & Sen, K. (2007). Cortical discrimination of complex natural stimuli: Can single neurons match behavior? Journal of Neuroscience, 27, 582–589.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of MathematicsTrinity College DublinDublin 2Ireland

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