On the Christoffel function and classification in data analysis

Jean B. Lasserre

doi:10.5802/crmath.358

Algorithmic and computer tools

On the Christoffel function and classification in data analysis

Jean B. Lasserre ¹

¹ LAAS-CNRS and Institute of Mathematics, BP 54200, 7 Avenue du Colonel Roche, 31031 Toulouse cédex 4, France

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 919-928.

Abstract
Résumé

We show that the empirical Christoffel function associated with a cloud of finitely many points sampled from a distribution, can provide a simple tool for supervised classification in data analysis, with good generalization properties.

Nous montrons que la fonction de Christoffel empirique associée à un échantillon fini de points peut fournir un outil simple pour la classification supervisée en analyse de données, avec de bonnes propriétés de généralisation.

Received: 2022-03-16
Revised: 2022-03-21
Accepted: 2022-03-21
Published online: 2022-09-14

DOI: 10.5802/crmath.358

Classification: 41A30, 42C05, 47B32, 68T09, 94A16

Author's affiliations:

Jean B. Lasserre ¹

¹ LAAS-CNRS and Institute of Mathematics, BP 54200, 7 Avenue du Colonel Roche, 31031 Toulouse cédex 4, France

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {On the {Christoffel} function and classification in data analysis},
     journal = {Comptes Rendus. Math\'ematique},
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     year = {2022},
     doi = {10.5802/crmath.358},
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Jean B. Lasserre. On the Christoffel function and classification in data analysis. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 919-928. doi : 10.5802/crmath.358. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.358/

References
Cited by

[1] Steven L. Brunton; J. Nathan Kutz Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control, Cambridge University Press, 2019

[2] Jean Bernard Lasserre; Edouard Pauwels Sorting out typicality via the inverse moment matrix SOS polynomial, Advances in Neural Information Processing Systems (2016), pp. 190-198

[3] Jean Bernard Lasserre; Edouard Pauwels The empirical Christoffel function with applications in data analysis, Adv. Comput. Math., Volume 45 (2019) no. 3, pp. 1439-1468

[4] Jean Bernard Lasserre; Edouard Pauwels; Mihai Putinar The Christoffel–Darboux Kernel for Data Analysis, Cambridge Monographs on Applied and Computational Mathematics, 38, Cambridge University Press, 2022 | Zbl

[5] Swann Marx; Edouard Pauwels; Tillmann Weisser; Didier Henrion; Jean Bernard Lasserre Semi-algebraic approximation using Christoffel–Darboux kernel, Constr. Approx., Volume 54 (2021) no. 3, pp. 391-429

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