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

By Frédéric Chazal, Bertrand Michel. Frontiers in Artificial Intelligence, 2017

820 citations recorded by the source corpus.

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.

Subfields: Biophysics, Computational Theory and Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/aff16209e232d38fc94a5b0c72067b88d106453f

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Citations in the corpus

What are higher-order networks? (2021, methodology): “Persistent homology is computable, with many software implementations available, and we refer to the following tutorials and “user guides” to more information [68,217,230,235,243].”
Networks beyond pairwise interactions: structure and dynamics (2020, neutral): “[265] Frédéric Chazal and Bertrand Michel.”
Informed Machine Learning – A Taxonomy and Survey of Integrating Prior Knowledge into Learning Systems (2019, background): “Geometric properties, invariants and symmetries of the data are the central topic of fields such as geometric learning [136] and topological data analysis [143].”
Persistent Convolution: A Topological Framework for AI Alignment Testing and Semantic Space Characterization (2026, unknown): “Theorem 2.2 (Nerve Theorem, Chazal and Michel, 2021) .”