The Christoffel-Darboux Kernel for Data Analysis
Jean Bernard Lasserre  1, 2@  
1 : Laboratoire d'analyse et d'architecture des systèmes [Toulouse]  (LAAS)  -  Site web
Institut National Polytechnique de Toulouse - INPT, Université Paul Sabatier (UPS) - Toulouse III, CNRS : UPR8001, Institut National des Sciences Appliquées [INSA] - Toulouse
7 Av du colonel Roche 31077 TOULOUSE CEDEX 4 -  France
2 : Institut de Mathématiques de Toulouse  (IMT)
PRES Université de Toulouse, CNRS : UMR5219
UPS IMT, F-31062 Toulouse Cedex 9, France INSA, F-31077 Toulouse, France UT1, F-31042 Toulouse, France UT2, F-31058 Toulouse, France -  France

If the Christoffel-Darboux (CD) kernel is well-known in theory of approximation and orthogonal polynomials, its striking properties seem to have been largely ignored in the context of data analysis (one main reason being that in data analysis one is faced with measures supported on finitely many points (the data set)). In this talk, we briefly introduce the (CD) kernel, some of its properties, and claim that it can become a simple and easy to use tool in the context of data analysis, e.g. to help solve some problems like outlier detection, manifold learning and density estimation.


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