Spike Metrics

Part of the Springer Series in Computational Neuroscience book series (NEUROSCI, volume 7)


Important questions in neuroscience, such as how neural activity represents the sensory world, can be framed in terms of the extent to which spike trains differ from one another. Since spike trains can be considered to be sequences of stereotyped events, it is natural to focus on ways to quantify differences between event sequences, known as spike-train metrics. We begin by defining several families of these metrics, including metrics based on spike times, on interspike intervals, and on vector-space embedding. We show how these metrics can be applied to single-neuron and multineuronal data and then describe algorithms that calculate these metrics efficiently. Finally, we discuss analytical procedures based on these metrics, including methods for quantifying variability among spike trains, for constructing perceptual spaces, for calculating information-theoretic quantities, and for identifying candidate features of neural codes.


Mutual Information Spike Train Dynamic Programming Algorithm Elementary Step Interspike Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abbott LF (2000) Integrating with action potentials. Neuron 26:3–4 CrossRefPubMedGoogle Scholar
  2. Abeles M (1982) Role of the cortical neuron: integrator or coincidence detector?. Isr J Med Sci 18:83–92 PubMedGoogle Scholar
  3. Abeles M, Prut Y (1996) Spatio-temporal firing patterns in the frontal cortex of behaving monkeys. J Physiol Paris 90:249–250 CrossRefPubMedGoogle Scholar
  4. Aronov D (2003) Fast algorithm for the metric-space analysis of simultaneous responses of multiple single neurons. J Neurosci Methods 124:175–179 CrossRefPubMedGoogle Scholar
  5. Aronov D, Victor JD (2004) Non-Euclidean properties of spike train metric spaces. Phys Rev E Stat Nonlin Soft Matter Phys 69:061905 CrossRefPubMedGoogle Scholar
  6. Aronov D, Reich DS, Mechler F, Victor JD (2003) Neural coding of spatial phase in V1 of the macaque monkey. J Neurophysiol 89:3304–3327 CrossRefPubMedGoogle Scholar
  7. Banerjee A, Series P, Pouget A (2008) Dynamical constraints on using precise spike timing to compute in recurrent cortical networks. Neural Comput 20:974–993 CrossRefPubMedGoogle Scholar
  8. Carlton AG (1969) On the bias of information estimates. Psychol Bull 71:108–109 CrossRefGoogle Scholar
  9. Chichilnisky EJ, Rieke F (2005) Detection sensitivity and temporal resolution of visual signals near absolute threshold in the salamander retina. J Neurosci 25:318–330 CrossRefPubMedGoogle Scholar
  10. Coifman RR, Lafon S, Lee AB, Maggioni M, Nadler B, Warner F, Zucker SW (2005) Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. Proc Natl Acad Sci USA 102:7426–7431 CrossRefPubMedGoogle Scholar
  11. Cover TM, Thomas JA (1991) Elements of information theory, Schilling DL (ed). Wiley, New York CrossRefGoogle Scholar
  12. Dan Y, Poo MM (2004) Spike timing-dependent plasticity of neural circuits. Neuron 44:23–30 CrossRefPubMedGoogle Scholar
  13. Di Lorenzo PM, Victor JD (2003) Taste response variability and temporal coding in the nucleus of the solitary tract of the rat. J Neurophysiol 90:1418–1431 CrossRefPubMedGoogle Scholar
  14. Di Lorenzo PM, Victor JD (2007) Neural coding mechanisms for flow rate in taste-responsive cells in the nucleus of the solitary tract of the rat. J Neurophysiol 97:1857–1861 CrossRefPubMedGoogle Scholar
  15. Di Lorenzo PM, Chen J-Y, Victor JD (2009) Quality time: representation of a multidimensional sensory domain through temporal coding. J Neurosci 29(29):9227–9238 CrossRefPubMedGoogle Scholar
  16. Dubbs AJ, Seiler BA, Magnasco MO (2009) A fast Lp spike alignment metric. arXiv:0907.3137v2
  17. Egger V, Feldmeyer D, Sakmann B (1999) Coincidence detection and changes of synaptic efficacy in spiny stellate neurons in rat barrel cortex. Nat Neurosci 2:1098–1105 CrossRefPubMedGoogle Scholar
  18. Erickson RP (1984) Ohrwall, Henning and von Skramlik; the foundations of the four primary positions in taste. Neurosci Biobehav Rev 8:105–127 CrossRefPubMedGoogle Scholar
  19. Furukawa S, Middlebrooks JC (2002) Cortical representation of auditory space: information-bearing features of spike patterns. J Neurophysiol 87:1749–1762 PubMedGoogle Scholar
  20. Gaal SA (1964) Point set topology. Academic Press, New York Google Scholar
  21. Goldberg DH, Victor JD, Gardner EP, Gardner D (2009) Spike train analysis toolkit: enabling wider application of information-theoretic techniques to neurophysiology. Neuroinformatics 7(3):165–178 CrossRefPubMedGoogle Scholar
  22. Grewe J, Kretzberg J, Warzecha AK, Egelhaaf M (2003) Impact of photon noise on the reliability of a motion-sensitive neuron in the fly’s visual system. J Neurosci 23:10776–10783 PubMedGoogle Scholar
  23. Hopfield JJ (1995) Pattern recognition computation using action potential timing for stimulus representation. Nature 376:33–36 CrossRefPubMedGoogle Scholar
  24. Houghton C. (2009) Studying spike trains using a van Rossum metric with a synapse-like filter. J Computat Neurosci 26:149–155 CrossRefGoogle Scholar
  25. Houghton C, Sen K (2008) A new multineuron spike train metric. Neural Comput 20(6) 1495–1511 CrossRefPubMedGoogle Scholar
  26. Jacobs AL, Fridman G, Douglas RM, Alam NM, Latham PE, Prusky GT, Nirenberg S (2009) Ruling out and ruling in neural codes. Proc Natl Acad Sci USA 106:5936–5941 CrossRefPubMedGoogle Scholar
  27. Keat J, Reinagel P, Reid RC, Meister M (2001) Predicting every spike: a model for the responses of visual neurons. Neuron 30:803–817 CrossRefPubMedGoogle Scholar
  28. Kreiman G, Krahe R, Metzner W, Koch C, Gabbiani F (2000) Robustness and variability of neuronal coding by amplitude-sensitive afferents in the weakly electric fish eigenmannia. J Neurophysiol 84:189–204 PubMedGoogle Scholar
  29. Kruskal JB, Wish M (1978) Multidimensional scaling. Sage, Beverly Hills Google Scholar
  30. Kuba H, Yamada R, Fukui I, Ohmori H (2005) Tonotopic specialization of auditory coincidence detection in nucleus laminaris of the chick. J Neurosci 25:1924–1934 CrossRefPubMedGoogle Scholar
  31. Lim D, Capranica RR (1994) Measurement of temporal regularity of spike train responses in auditory nerve fibers of the green treefrog. J Neurosci Methods 52:203–213 CrossRefPubMedGoogle Scholar
  32. Machens C, Prinz P, Stemmler M, Ronacher B, Herz A (2001) Discrimination of behaviorally relevant signals by auditory receptor neurons. Neurocomputing 38:263–268 CrossRefGoogle Scholar
  33. MacLeod K, Backer A, Laurent G (1998) Who reads temporal information contained across synchronized and oscillatory spike trains?. Nature 395:693–698 CrossRefPubMedGoogle Scholar
  34. Maloney LT, Yang JN (2003) Maximum likelihood difference scaling. J Vision 3:5. doi: 10.1167/3.8.5 CrossRefGoogle Scholar
  35. Markram H, Lubke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275:213–215 CrossRefPubMedGoogle Scholar
  36. Mechler F, Victor JD, Purpura KP, Shapley R (1998) Robust temporal coding of contrast by V1 neurons for transient but not for steady-state stimuli. J Neurosci 18:6583–6598 PubMedGoogle Scholar
  37. Middlebrooks JC, Clock AE, Xu L, Green DM (1994) A panoramic code for sound location by cortical neurons. Science 264:842–844 CrossRefPubMedGoogle Scholar
  38. Miller GA (1955) Note on the bias on information estimates. Information Theory in Psychology: Problems and Methods II-B:95–100 Google Scholar
  39. Needleman SB, Wunsch CD (1970) A general method applicable to the search for similarities in the amino acid sequence of two proteins. J Mol Biol 48:443–453 CrossRefPubMedGoogle Scholar
  40. Nelken I (2009) Personal communication Google Scholar
  41. Nemenman I, Bialek W, de Ruyter van Steveninck R (2004) Entropy and information in neural spike trains: progress on the sampling problem. Phys Rev E Stat Nonlin Soft Matter Phys 69:056111 CrossRefPubMedGoogle Scholar
  42. Paninski L (2003) Estimation of entropy and mutual information. Neural Comput 15:1191 CrossRefGoogle Scholar
  43. Reich D, Mechler F, Victor J (2000) Temporal coding of contrast in primary visual cortex: when, what, and why?. J Neurophysiol 85:1039–1050 Google Scholar
  44. Reinagel P, Reid RC (2002) Precise firing events are conserved across neurons. J Neurosci 22:6837–6841 PubMedGoogle Scholar
  45. Richmond BJ, Optican LM (1987) Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. II. Quantification of response waveform. J Neurophysiol 57:147–161 PubMedGoogle Scholar
  46. Rieke F, Warland D, de Ruyter van Steveninck R, Bialek W (1997) Spikes: exploring the neural code. MIT Press, Cambridge Google Scholar
  47. Samonds JM, Bonds AB (2004) From another angle: differences in cortical coding between fine and coarse discrimination of orientation. J Neurophysiol 91:1193–1202 CrossRefPubMedGoogle Scholar
  48. Samonds JM, Allison JD, Brown HA, Bonds AB (2003) Cooperation between area 17 neuron pairs enhances fine discrimination of orientation. J Neurosci 23:2416–2425 PubMedGoogle Scholar
  49. Schreiber S, Fellous JM, Tiesinga P, Sejnowski TJ (2004) Influence of ionic conductances on spike timing reliability of cortical neurons for suprathreshold rhythmic inputs. J Neurophysiol 91:194–205 CrossRefPubMedGoogle Scholar
  50. Segundo JP, Perkel DH (1969) The nerve cell as an analyzer of spike trains. In: Brazier MAB (ed) The interneuron. University of California Press, Berkeley, pp 349–390 Google Scholar
  51. Sellers P (1974) On the theory and computation of evolutionary distances. SIAM J Appl Math 26:787–793 CrossRefGoogle Scholar
  52. Sen K, Jorge-Rivera JC, Marder E, Abbott LF (1996) Decoding synapses. J Neurosci 16:6307–6318 PubMedGoogle Scholar
  53. Shannon CE, Weaver W (1949) The mathematical theory of communication. University of Illinois Press, Urbana Google Scholar
  54. Singh G, Memoli F, Ishkhanov T, Sapiro G, Carlsson G, Ringach DL (2008) Topological analysis of population activity in visual cortex. J Vision 8:1–18 CrossRefGoogle Scholar
  55. Slepian D (1976) On bandwidth. Proc IEEE 64:292–300 CrossRefGoogle Scholar
  56. Softky WR, Koch C (1993) The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J Neurosci 13:334–350 PubMedGoogle Scholar
  57. Stopfer M, Bhagavan S, Smith BH, Laurent G (1997) Impaired odour discrimination on desynchronization of odour-encoding neural assemblies. Nature 390:70–74 CrossRefPubMedGoogle Scholar
  58. Tenenbaum JB, de Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290:2319–2323 CrossRefPubMedGoogle Scholar
  59. Tiesinga PHE (2004) Chaos-induced modulation of reliability boosts output firing rate in downstream cortical areas. Phys Rev E Stat Nonlin Soft Matter Phys 69:031912 CrossRefPubMedGoogle Scholar
  60. Treves A, Panzeri S (1995) The upward bias in measures of information derived from limited data samples. Neural Comput 7:399–407 CrossRefGoogle Scholar
  61. Tversky A (1977) Features of similarity. Psychol Rev 84:327–352 CrossRefGoogle Scholar
  62. Tversky A, Gati I (1982) Similarity, separability, and the triangle inequality. Psychol Rev 89:123–154 CrossRefPubMedGoogle Scholar
  63. van Rossum MC (2001) A novel spike distance. Neural Comput 13:751–763 CrossRefPubMedGoogle Scholar
  64. Victor JD (2000) Asymptotic bias in information estimates and the exponential (Bell) polynomials. Neural Comput 12:2797–2804 CrossRefPubMedGoogle Scholar
  65. Victor JD (2002) Binless strategies for estimation of information from neural data. Phys Rev E 66:51903 CrossRefGoogle Scholar
  66. Victor JD (2006) Approaches to information-theoretic analysis of neural activity. Biological Theory 1:302–316 CrossRefPubMedGoogle Scholar
  67. Victor JD, Purpura KP (1996) Nature and precision of temporal coding in visual cortex: a metric-space analysis. J Neurophysiol 76:1310–1326 PubMedGoogle Scholar
  68. Victor JD, Purpura KP (1997) Metric-space analysis of spike trains: theory, algorithms and application. Network 8:127–164 CrossRefGoogle Scholar
  69. Victor JD, Goldberg DH, Gardner D (2007) Dynamic programming algorithms for comparing multineuronal spike trains via cost-based metrics and alignments. J Neurosci Methods 161:351–360 CrossRefPubMedGoogle Scholar
  70. Wu L, Gotman J (1998) Segmentation and classification of EEG during epileptic seizures. Electroencephalogr Clin Neurophysiol 106:344–356 CrossRefPubMedGoogle Scholar
  71. Wuerger SM, Maloney LT, Krauskopf J (1995) Proximity judgments in color space: tests of a Euclidean color geometry. Vision Res 35:827–835 CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Division of Systems Neurology and Neuroscience, Department of Neurology and NeuroscienceWeill Cornell Medical CollegeNew YorkUSA

Personalised recommendations