Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System

Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain's spatial representation sys...

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Bibliographic Details
Published in:Frontiers in computational neuroscience 2021-04, Vol.15, p.616748-616748
Main Authors: Kang, Louis, Xu, Boyan, Morozov, Dmitriy
Format: Article
Language:English
Subjects:
Data analysis
Datasets
dimensionality reduction
grid cells
Homology
Nervous system
neural decoding
neural manifold
Neurons
Neuroscience
Simulation
spatial representation
Time series
topological data analysis
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Summary:Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain's spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.
ISSN:1662-5188
1662-5188
DOI:10.3389/fncom.2021.616748