AUTHOR=Chazal Frédéric , Michel Bertrand TITLE=An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists JOURNAL=Frontiers in Artificial Intelligence VOLUME=Volume 4 - 2021 YEAR=2021 URL=https://www.frontiersin.org/journals/artificial-intelligence/articles/10.3389/frai.2021.667963 DOI=10.3389/frai.2021.667963 ISSN=2624-8212 ABSTRACT=

With the recent explosion in the amount, the variety, and the dimensionality of available data, identifying, extracting, and exploiting their underlying structure has become a problem of fundamental importance for data analysis and statistical learning. Topological data analysis (tda) is a recent and fast-growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. It proposes new well-founded mathematical theories and computational tools that can be used independently or in combination with other data analysis and statistical learning techniques. This article is a brief introduction, through a few selected topics, to basic fundamental and practical aspects of tda for nonexperts.