Topological data analysis and machine learning

Abstract

Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest among physicists. We present a concise yet (we hope) comprehensive review of applications of topological data analysis to physics and machine learning problems in physics including the detection of phase transitions. We finish with a preview of anticipated directions for future research.

arXiv commentInvited review, 15 pages, 7 figures, 117 references

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Cited by in corpus (6)

• Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model
• Topological Data Analysis of Monopole Current Networks in $U(1)$ Lattice Gauge Theory
• Identifying weak critical fluctuations of intermittency in heavy-ion collisions with topological machine learning
• Random sequential covering of a one-dimensional lattice by $k$-mers
• Modeling and Simulating Dependence in Networks Using Topological Data Analysis
• Multiscale geometrical and topological learning in the analysis of soft matter collective dynamics