🍩 Database of Original & Non-Theoretical Uses of Topology

1. Interpretable Phase Detection and Classification With Persistent Homology (2020)

   Alex Cole, Gregory J. Loges, Gary Shiu

   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.

   • URL
   • Export citation

   • Condensed matter
   • Machine learning
   • Phase transition
   • Lattice configurations
   • Point cloud
   • Spin configurations
   • Logistic regression
   • Persistent homology