no. G8
Algorithmes et outils informatiques
On the Christoffel function and classification in data analysis
Lasserre, Jean B.1
1 LAAS-CNRS and Institute of Mathematics, BP 54200, 7 Avenue du Colonel Roche, 31031 Toulouse cédex 4, France
Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 919-928.

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.

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.

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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, Tome 360 (2022) no. G8, pp. 919-928. doi : 10.5802/crmath.358. http://www.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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