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      An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists

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          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.

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            The NumPy Array: A Structure for Efficient Numerical Computation

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              Data Structures for Statistical Computing in Python

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                Author and article information

                Contributors
                Journal
                Front Artif Intell
                Front Artif Intell
                Front. Artif. Intell.
                Frontiers in Artificial Intelligence
                Frontiers Media S.A.
                2624-8212
                29 September 2021
                2021
                : 4
                : 667963
                Affiliations
                [ 1 ]Inria Saclay - Île-de-France Research Centre, Palaiseau, France
                [ 2 ]Ecole Centrale de Nantes, Nantes, France
                Author notes

                Edited by: Sriraam Natarajan, The University of Texas at Dallas, United States

                Reviewed by: Ajey Kumar, Symbiosis International (Deemed University), India

                Devendra Singh Dhami, Darmstadt University of Technology, Germany

                *Correspondence: Bertrand Michel, bertrand.michel@ 123456ec-nantes.fr

                This article was submitted to Machine Learning and Artificial Intelligence, a section of the journal Frontiers in Artificial Intelligence

                Article
                667963
                10.3389/frai.2021.667963
                8511823
                34661095
                a26e292f-0dd1-4eb1-9b93-40bc487f7d6c
                Copyright © 2021 Chazal and Michel.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                History
                : 15 February 2021
                : 16 July 2021
                Categories
                Artificial Intelligence
                Review

                topological data analysis,machine learning,geometric inference,topological inference,statistic

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