Neural Computing and Applications

, Volume 19, Issue 3, pp 405–419 | Cite as

A comparison of binless spike train measures

  • António R. C. Paiva
  • Il Park
  • José C. Príncipe
Original Article

Abstract

Several binless spike train measures which avoid the limitations of binning have been recently been proposed in the literature. This paper presents a systematic comparison of these measures in three simulated paradigms designed to address specific situations of interest in spike train analysis where the relevant feature may be in the form of firing rate, firing rate modulations, and/or synchrony. The measures are first disseminated and extended for ease of comparison. It also discusses how the measures can be used to measure dissimilarity in spike trains' firing rate despite their explicit formulation for synchrony.

Keywords

Distance measures Spike train analysis 

References

  1. 1.
    Victor JD, Purpura KP (1996) Nature and precision of temporal coding in visual cortex: a metric-space analysis. J Neurophysiol 76(2):1310–1326Google Scholar
  2. 2.
    Victor JD, Purpura KP (1997) Metric-space analysis of spike trains: theory, algorithms, and application. Netw Comp Neural Syst 8:127–164MATHCrossRefGoogle Scholar
  3. 3.
    Wohlgemuth S, Ronacher B (2007) Auditory discrimination of amplitude modulations based on metric distances of spike trains. J Neurophysiol 97:3082–3092. doi:10.1152/jn.01235.2006 CrossRefGoogle Scholar
  4. 4.
    Houghton C (2009) Studying spike trains using a van Rossum metric with a synapse-like filter. J Comp Neurosci 26:149–155. doi:10.1007/s10827-008-0106-6 CrossRefMathSciNetGoogle Scholar
  5. 5.
    Brown EN, Kass RE, Mitra PP (2004) Multiple neural spike train data analysis: state-of-the-art and future challenges. Nature Neurosci 7:456–461. doi:10.1038/nn1228 CrossRefGoogle Scholar
  6. 6.
    Dayan P, Abbott LF (2001) Theoretical neuroscience: computational and mathematical modeling of neural systems. MIT Press, CambridgeMATHGoogle Scholar
  7. 7.
    Rieke F, Warland D, van Steveninck RR, Bialek W (1999) Spikes: exploring the neural code. MIT Press, Cambridge. ISBN 0-262-18174-6Google Scholar
  8. 8.
    Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocortical neurons. Science 268(5216):1503–1506. doi:10.1126/science.7770778 CrossRefGoogle Scholar
  9. 9.
    Hatsopoulos NG, Ojakangas CL, Paninski L, Donoghue JP (1998) Information about movement direction obtained from synchronous activity of motor cortical neurons. Proc Natl Acad Sci 95(26):15706–15711CrossRefGoogle Scholar
  10. 10.
    Wagner H, Brill S, Kempter R, Carr CE (2005) Microsecond precision of phase delay in the auditory system of the barn owl. J Neurophysiol 94(2):1655–1658. doi:10.1152/jn.01226.2004 CrossRefGoogle Scholar
  11. 11.
    Eggermont JJ (2006) Properties of correlated neural activity clusters in cat auditory cortex resemble those of neural assemblies. J Neurophysiol 96(2):746–764. doi:10.1152/jn.00059.2006 Google Scholar
  12. 12.
    Riehle A, Grün S, Diesmann M, Aertsen A (1997) Spike synchronization and rate modulation differentially involved in motor cortical function. Science 278(5345):1950–1953. doi:10.1126/science.278.5345.1950 CrossRefGoogle Scholar
  13. 13.
    Grün S, Diesmann M, Aertsen A (2002) Unitary Events in multiple single-neuron activity. I. detection and significance. Neural Comp 14(1):43–80MATHCrossRefGoogle Scholar
  14. 14.
    Grün S, Diesmann M, Aertsen A (2002) Unitary Events in multiple single-neuron activity. II. nonstationary data. Neural Comp 14(1):43–80MATHCrossRefGoogle Scholar
  15. 15.
    Grün S, Diesmann M, Grammont F, Riehle A, Aertsen A (1999) Detecting unitary events without discretization of time. J Neurosci Methods 93(1):67–79. doi:10.1016/S0165-0270(99)00126-0 CrossRefGoogle Scholar
  16. 16.
    van Rossum MCW (2001) A novel spike distance. Neural Comp 13(4):751–764MATHCrossRefGoogle Scholar
  17. 17.
    Schreiber S, Fellous JM, Whitmer D, Tiesinga P, Sejnowski TJ (2003) A new correlation-based measure of spike timing reliability. Neurocomp 52–54:925–931. doi:10.1016/S0925-2312(02)00838-X CrossRefGoogle Scholar
  18. 18.
    Kreuz T, Haas JS, Morelli A, Abarbanel HDI, Politi A (2007) Measuring spike train synchrony. J Neurosci Methods 165(1):151–161. doi:10.1016/j.jneumeth.2007.05.031 CrossRefGoogle Scholar
  19. 19.
    Hunter JD, Milton JG (2003) Amplitude and frequency dependence of spike timing: Implications for dynamic regulation. J Neurophysiol 90(1):387–394. doi:10.1152/jn.00074.2003 CrossRefGoogle Scholar
  20. 20.
    Aronov D, Reich DS, Mechler F, Victor JD (2003) Neural coding of spatial phase in V1 of the macaque monkey. J Neurophysiol 89(6):3304–3327. doi:10.1152/jn.00826.2002 CrossRefGoogle Scholar
  21. 21.
    Aronszajn N (1950) Theory of reproducing kernels. Trans Am Math Soc 68(3):337–404MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Houghton C, Sen K (2008) A new multineuron spike train metric. Neural Comp 20(6):1495–1511. doi:10.1162/neco.2007.10-06-350 MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Victor JD (2005) Spike train metrics. Curr Opin Neurobiol 15(5):585–592. doi:10.1016/j.conb.2005.08.002 CrossRefGoogle Scholar
  24. 24.
    Fellous J-M, Tiesinga PHE, Thomas PJ, Sejnowski TJ (2004) Discovering spike patterns in neuronal responses. J Neurosci 24(12):2989–3001. doi:10.1523/JNEUROSCI.4649-03.2004 CrossRefGoogle Scholar
  25. 25.
    Paiva ARC, Rao S, Park I, Príncipe JC (2007) Spectral clustering of synchronous spike trains. In: Proceedings of the IEEE international joint conference on neural networks, IJCNN-2007, Orlando, FL, USAGoogle Scholar
  26. 26.
    Toups JV, Tiesinga PHE (2006) Methods for finding and validating neural spike patterns. Neurocomputing 69(10–12):1362–1365CrossRefGoogle Scholar
  27. 27.
    Schrauwen B, Van Campenhout J (2007) Linking non-binned spike train kernels to several existing spike train distances. Neurocomputing 70(7–8):1247–1253. doi:10.1016/j.neucom.2006.11.017 CrossRefGoogle Scholar
  28. 28.
    Wang L, Narayan R, Graña G, Shamir M, Sen K (2007) Cortical discrimination of complex natural stimuli: can single neurons match behavior? J Neurosci 27(3):582–589. doi:10.1523/JNEUROSCI.3699-06.2007 CrossRefGoogle Scholar
  29. 29.
    Abeles M (1991) Corticonics: neural circuits of the cerebral cortex. Cambridge University Press, New YorkGoogle Scholar
  30. 30.
    Shadlen MN, Newsome WT (1994) Noise, neural codes and cortical organization. Curr Opin Neurobiol 4(4):569–579CrossRefGoogle Scholar
  31. 31.
    de Ruyter van Steveninck RR, Lewen GD, Strong SP, Koberle R, Bialek W (1997) Reproducibility and variability in neural spike trains. Science 275:1805–1808CrossRefGoogle Scholar
  32. 32.
    Papoulis A (1965) Probability, random variables, and stochastic processes. McGraw-Hill, New YorkMATHGoogle Scholar
  33. 33.
    Reiss R-D (1993) A course on point processes. Springer, New YorkMATHGoogle Scholar
  34. 34.
    Paiva ARC, Park I, Príncipe JC (2009) A reproducing kernel Hilbert space framework for spike train signal processing. Neural Comp 21(2):424–449. doi:10.1162/neco.2008.09-07-614 MATHCrossRefGoogle Scholar
  35. 35.
    Pekalska E, Duin RPW (2005) The dissimilarity representation for pattern recognition: foundations and applications. World Scientific, Singapore. ISBN 9-812-56530-3MATHCrossRefGoogle Scholar
  36. 36.
    Duda RO, Hart PE, Stork DG (2000) Pattern classification, 2nd edn. Wiley InterscienceGoogle Scholar
  37. 37.
    Adrian ED (1928) The basis of sensation: the action of the sense organs. W. W. Norton & Co., New YorkGoogle Scholar
  38. 38.
    Kuhn A, Aertsen A, Rotter S (2003) Higher-order statistics of input ensembles and the response of simple model neurons. Neural Comp 15(1):67–101MATHCrossRefGoogle Scholar
  39. 39.
    Kuhn A, Rotter S, Aertsen A (2002) Correlated input spike trains and their effects on the response of the leaky integrate-and-fire neuron. Neurocomputing 44–46:121–126. doi:10.1016/S0925-2312(02)00372-7 CrossRefGoogle Scholar
  40. 40.
    Narayan R, Graña G, Sen K (2006) Distinct time scales in cortical discrimination of natural sounds in songbirds. J Neurophysiol 96(1):252–258. doi:10.1152/jn.01257.2005 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  • António R. C. Paiva
    • 1
  • Il Park
    • 1
  • José C. Príncipe
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of FloridaGainesvilleUSA

Personalised recommendations