Interpretable Phase Detection and Classification with Persistent Homology
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
Text
Loges et al. "Interpretable Phase Detection and Classification with Persistent Homology." NeurIPS 2020 Workshops: TDA_and_Beyond, 2020.Markdown
[Loges et al. "Interpretable Phase Detection and Classification with Persistent Homology." NeurIPS 2020 Workshops: TDA_and_Beyond, 2020.](https://mlanthology.org/neuripsw/2020/loges2020neuripsw-interpretable/)BibTeX
@inproceedings{loges2020neuripsw-interpretable,
title = {{Interpretable Phase Detection and Classification with Persistent Homology}},
author = {Loges, Gregory and Cole, Alex and Shiu, Gary},
booktitle = {NeurIPS 2020 Workshops: TDA_and_Beyond},
year = {2020},
url = {https://mlanthology.org/neuripsw/2020/loges2020neuripsw-interpretable/}
}