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Using persistent homology to reveal hidden covariates in systems governed by the kinetic Ising model

Gard Spreemann1,*, Benjamin Dunn2, Magnus Bakke Botnan1,†, and Nils A. Baas1

  • 1Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim 7491, Norway
  • 2Kavli Institute for Systems Neuroscience, Norwegian University of Science and Technology, Trondheim 7491, Norway

  • *gard.spreemann@epfl.ch; Present address: Laboratory for Topology and Neuroscience, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
  • †Present address: Lehrstuhl für Geometrie und Visualisierung, Technische Universität München, 85748 Garching bei München, Germany.
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Phys. Rev. E 97, 032313 – Published 26 March, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.032313

Abstract

We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates in a system governed by the kinetic Ising model with time-varying external fields. As its starting point the method takes observations of the system under study, a list of suspected or known covariates, and observations of those covariates. We infer away the contributions of the suspected or known covariates, after which persistent homology reveals topological information about unknown remaining covariates. Our motivating example system is the activity of neurons tuned to the covariates physical position and head direction, but the method is far more general.

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Phys. Rev. E 97, 032313– Published 26 March, 2018
  • Received 2 October 2017
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