PMID: 15244615Jul 13, 2004Paper

Non-Euclidean properties of spike train metric spaces

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Dmitriy Aronov, Jonathan D Victor

Abstract

Quantifying the dissimilarity (or distance) between two sequences is essential to the study of action potential (spike) trains in neuroscience and genetic sequences in molecular biology. In neuroscience, traditional methods for sequence comparisons rely on techniques appropriate for multivariate data, which typically assume that the space of sequences is intrinsically Euclidean. More recently, metrics that do not make this assumption have been introduced for comparison of neural activity patterns. These metrics have a formal resemblance to those used in the comparison of genetic sequences. Yet the relationship between such metrics and the traditional Euclidean distances has remained unclear. We show, both analytically and computationally, that the geometries associated with metric spaces of event sequences are intrinsically non-Euclidean. Our results demonstrate that metric spaces enrich the study of neural activity patterns, since accounting for perceptual spaces requires a non-Euclidean geometry.

References

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Jan 7, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jonathan D Victor
Mar 4, 2003·Journal of Neurophysiology·Dmitriy AronovJonathan D Victor

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Citations

Nov 18, 2008·Biological cybernetics·Renaud JolivetArnd Roth
Jul 9, 2008·Journal of Computational Neuroscience·Conor Houghton
May 18, 2011·Journal of Computational Neuroscience·Wei Wu, Anuj Srivastava
Oct 12, 2012·Journal of Computational Neuroscience·Wei Wu, Anuj Srivastava
Nov 26, 2010·Journal of Neurophysiology·Jen-Yung ChenPatricia M Di Lorenzo
Nov 30, 2007·Neural Computation·Vladimir ItskovKenneth D Harris
Sep 2, 2010·Neural Computation·Alexander J DubbsMarcelo O Magnasco
May 22, 2010·Neural Networks : the Official Journal of the International Neural Network Society·Sonja B HoferNicholas A Lesica
Dec 28, 2007·Journal of Neuroscience Methods·Renaud JolivetWulfram Gerstner
Dec 19, 2006·Journal of Neuroscience Methods·Jonathan D VictorDaniel Gardner
Sep 6, 2005·Current Opinion in Neurobiology·Jonathan D Victor
May 24, 2011·Journal of Neuroscience Methods·David Lyttle, Jean-Marc Fellous
May 28, 2017·Vision Research·Jonathan D VictorMary M Conte
Jun 12, 2014·Journal of Computational Neuroscience·Pedro D Maia, J Nathan Kutz
Dec 24, 2018·Neural Computation·Conor Houghton

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