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.

Invited review, 15 pages, 7 figures, 117 references

References in corpus (29)

• Persistent Homology of Complex Networks
• Topological Methods for Exploring Low-density States in Biomolecular Folding Pathways
• Experimental Deep Reinforcement Learning for Error-Robust Gateset Design on a Superconducting Quantum Computer
• Quantitative and Interpretable Order Parameters for Phase Transitions from Persistent Homology
• Quantum algorithm for persistent Betti numbers and topological data analysis
• Unsupervised and supervised learning of interacting topological phases from single-particle correlation functions
• Identifying Topological Phase Transitions in Experiments Using Manifold Learning
• Homology and symmetry breaking in Rayleigh-Benard convection: Experiments and simulations
• Finding hidden order in spin models with persistent homology
• Machine-learning enhanced dark soliton detection in Bose-Einstein condensates
• Betti number signatures of homogeneous Poisson point processes
• Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
• Learning quantum phase transitions through Topological Data Analysis
• Temporal Network Analysis Using Zigzag Persistence
• An Introduction to Topological Data Analysis for Physicists: From LGM to FRBs
• Unsupervised learning of topological phase diagram using topological data analysis
• Quantum Topological Data Analysis with Linear Depth and Exponential Speedup
• A streamlined quantum algorithm for topological data analysis with exponentially fewer qubits
• Photonic band structure design using persistent homology
• Unsupervised machine learning approaches to the $q$-state Potts model
• Persistent Homology of ${\mathbb{Z}}_2$ Gauge Theories
• Persistent homology analysis of a generalized Aubry-André-Harper model
• Topological data analysis on noisy quantum computers
• Persistent homology of quantum entanglement
• Quantum Persistent Homology
• Representation of the Fermionic Boundary Operator
• Quantum machine learning with subspace states
• Dark soliton detection using persistent homology
• Limitations of Clustering Using Quantum Persistent Homology

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