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.
| Comments: | Invited review, 15 pages, 7 figures, 117 references |
| Subjects: | Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ; Optics (physics.optics); Quantum Physics (quant-ph) |
| Cite as: | arXiv:2206.15075 [cond-mat.mes-hall] |
| (or arXiv:2206.15075v3 [cond-mat.mes-hall] for this version) | |
| https://doi.org/10.48550/arXiv.2206.15075 |
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DOI(s) linking to related resourcesFrom: Daniel Leykam [view email]
[v1] Thu, 30 Jun 2022 07:11:04 UTC (814 KB)
[v2] Thu, 4 May 2023 05:54:26 UTC (819 KB)
[v3] Tue, 25 Jul 2023 13:47:05 UTC (819 KB)
View a PDF of the paper titled Topological data analysis and machine learning, by Daniel Leykam and Dimitris G. Angelakis