Non-Euclidean properties of spike train metric spaces.
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.
Aronov
Dmitriy
D
Department of Biological Sciences, Columbia University, 1002 Fairchild, Mail Code 2436, 1212 Amsterdam Avenue, New York, New York 10027, USA. da2006@columbia.edu
Victor
Jonathan D
JD
D000200:Action Potentials / Q000502:physiology*; D003198:Computer Simulation; D008959:Models, Neurological; D015233:Models, Statistical; D009474:Neurons / Q000502:physiology*; D012815:Signal Processing, Computer-Assisted; D016008:Statistical Distributions; D009435:Synaptic Transmission / Q000502:physiology*