Interpretable Phase Detection and Classification with Persistent Homology

• URL: http://arxiv.org/abs/2012.00783v1
• Date: Tue, 1 Dec 2020 19:12:35 GMT
• Title: Interpretable Phase Detection and Classification with Persistent Homology
• Authors: Alex Cole, Gregory J. Loges, Gary Shiu
• Abstract summary: Persistence images provide a useful representation of the homological data for conducting statistical tasks. To identify the phase transitions, a simple logistic regression on these images is sufficient for the models we consider. Magnetization, frustration and vortex-antivortex structure are identified as relevant features for characterizing phase transitions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We apply persistent homology to the task of discovering and characterizing phase transitions, using lattice spin models from statistical physics for working examples. Persistence images provide a useful representation of the homological data for conducting statistical tasks. To identify the phase transitions, a simple logistic regression on these images is sufficient for the models we consider, and interpretable order parameters are then read from the weights of the regression. Magnetization, frustration and vortex-antivortex structure are identified as relevant features for characterizing phase transitions.

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