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Evaluating state space discovery by persistent cohomology in the spatial representation system

View ORCID ProfileLouis Kang, Boyan Xu, View ORCID ProfileDmitriy Morozov
doi: https://doi.org/10.1101/2020.10.06.328773
Louis Kang
1Redwood Center for Theoretical Neuroscience, University of California, Berkeley
2Neural Circuits and Computations Unit, RIKEN Center for Brain Science
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  • For correspondence: louis.kang@riken.jp
Boyan Xu
3Department of Mathematics, University of California, Berkeley
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Dmitriy Morozov
4Computational Research Division, Lawrence Berkeley National Laboratory
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Abstract

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.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • ↵* louis.kang{at}riken.jp

  • ↵† boxu{at}berkeley.edu

  • ↵‡ dmitriy{at}mrzv.org

  • Expanded old Figures 3 and 4 into new Figures 3, 4, and 5; Added Supplementary Material

  • https://louiskang.group/repo

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
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Posted February 09, 2021.
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Evaluating state space discovery by persistent cohomology in the spatial representation system
Louis Kang, Boyan Xu, Dmitriy Morozov
bioRxiv 2020.10.06.328773; doi: https://doi.org/10.1101/2020.10.06.328773
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Evaluating state space discovery by persistent cohomology in the spatial representation system
Louis Kang, Boyan Xu, Dmitriy Morozov
bioRxiv 2020.10.06.328773; doi: https://doi.org/10.1101/2020.10.06.328773

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