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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| Published in | Frontiers in computational neuroscience Vol. 15; p. 616748 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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08.04.2021
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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. |
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| AbstractList | 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. |
| Author | Kang, Louis Morozov, Dmitriy Xu, Boyan |
| AuthorAffiliation | 4 Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, CA , United States 2 Neural Circuits and Computations Unit, RIKEN Center for Brain Science , Wako , Japan 1 Redwood Center for Theoretical Neuroscience, University of California, Berkeley , Berkeley, CA , United States 3 Department of Mathematics, University of California, Berkeley , Berkeley, CA , United States |
| AuthorAffiliation_xml | – name: 3 Department of Mathematics, University of California, Berkeley , Berkeley, CA , United States – name: 2 Neural Circuits and Computations Unit, RIKEN Center for Brain Science , Wako , Japan – name: 4 Computational Research Division, Lawrence Berkeley National Laboratory , Berkeley, CA , United States – name: 1 Redwood Center for Theoretical Neuroscience, University of California, Berkeley , Berkeley, CA , United States |
| Author_xml | – sequence: 1 givenname: Louis surname: Kang fullname: Kang, Louis organization: Neural Circuits and Computations Unit, RIKEN Center for Brain Science, Wako, Japan – sequence: 2 givenname: Boyan surname: Xu fullname: Xu, Boyan organization: Department of Mathematics, University of California, Berkeley, Berkeley, CA, United States – sequence: 3 givenname: Dmitriy surname: Morozov fullname: Morozov, Dmitriy organization: Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, United States |
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| Keywords | neural decoding neural manifold dimensionality reduction spatial representation topological data analysis grid cells medial entorhinal cortex |
| Language | English |
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| SubjectTerms | 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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| Title | Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System |
| URI | https://www.ncbi.nlm.nih.gov/pubmed/33897395 https://www.proquest.com/docview/2509896476 https://search.proquest.com/docview/2518735062 https://www.osti.gov/biblio/1774989 https://pubmed.ncbi.nlm.nih.gov/PMC8060447 https://doaj.org/article/ec9a068ec96e431f8f2f8c2091a12c74 |
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