Topological data analysis and machine learning

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 review of applications of topological data analysis to physics and machine learning problems in physics including the unsupervised detection of phase transitions. We finish with a preview of anticipated directions for future research.

Automated summary

Topological data analysis is a reliable and systematic method for computing abstract shapes of complex data sets, with applications in life and data sciences as well as growing interest among physicists. This article provides a concise review of its applications to physics and machine learning problems in physics, including unsupervised phase transition detection. The article also previews future research directions.