Interpretable Phase Detection and Classification with Persistent Homology
Statistical Mechanics
2020-12-03 v1 Machine Learning
Algebraic Topology
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.
Cite
@article{arxiv.2012.00783,
title = {Interpretable Phase Detection and Classification with Persistent Homology},
author = {Alex Cole and Gregory J. Loges and Gary Shiu},
journal= {arXiv preprint arXiv:2012.00783},
year = {2020}
}
Comments
5 pages, 3 figures; shortened version of arXiv:2009.14231; accepted to NeurIPS 2020 Workshop on Topological Data Analysis and Beyond