Clique topology reveals intrinsic geometric structure in neural correlations

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS Vol. 112; no. 44; pp. 13455 - 13460
Main Authors: Giusti, Chad, Pastalkova, Eva, Curto, Carina, Itskov, Vladimir
Format: Journal Article
Language:English
Published: United States 03.11.2015
Subjects:
Algorithms
Animals
Computer Simulation
Hippocampus - cytology
Hippocampus - physiology
Models, Neurological
Motor Activity - physiology
Neural Pathways - physiology
Neurophysiology - methods
Pyramidal Cells - physiology
Rats
Sleep, REM - physiology
structure of neural correlation
Betti curves
clique topology
neural coding
topological data analysis
ISSN:1091-6490
Online Access:Get more information
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Summary:Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.
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ISSN:1091-6490
DOI:10.1073/pnas.1506407112