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

• Published in: Frontiers in computational neuroscience Vol. 15; p. 616748
• Main Authors: Kang, Louis, Xu, Boyan, Morozov, Dmitriy
• Format: Journal Article
• Language: English
• Published: Switzerland Frontiers Research Foundation 08.04.2021; Frontiers Media SA; Frontiers Media S.A
• 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; neural decoding; neural manifold; dimensionality reduction; spatial representation; topological data analysis; grid cells; medial entorhinal cortex
• ISSN: 1662-5188; 1662-5188
• DOI: 10.3389/fncom.2021.616748

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.