Algorithmic and computer tools
On the Christoffel function and classification in data analysis
Comptes Rendus. Mathématique, Volume 360 (2022) no. G8, pp. 919-928.

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.

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DOI: 10.5802/crmath.358
Classification: 41A30, 42C05, 47B32, 68T09, 94A16
Lasserre, Jean B. 1

1 LAAS-CNRS and Institute of Mathematics, BP 54200, 7 Avenue du Colonel Roche, 31031 Toulouse cédex 4, France
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Lasserre, Jean B. On the Christoffel function and classification in data analysis. Comptes Rendus. Mathématique, Volume 360 (2022) no. G8, pp. 919-928. doi : 10.5802/crmath.358. http://archive.numdam.org/articles/10.5802/crmath.358/

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

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

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

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

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

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