# Interpretable Phase Detection and Classification with Persistent Homology

arXiv: https://arxiv.org/abs/2012.00783 · HTML: https://mlsanity.com/paper/2012.00783/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2020.

## Built on by (most cited first, 1 of 1)

- [Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds](https://mlsanity.com/paper/2310.19276/) (2023)

## Abstract (arXiv)

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.