Parameter selection for principal curves

Abstract : Principal curves are nonlinear generalizations of the notion of first principal component. Roughly, a principal curve is a parameterized curve in Rd which passes through the "middle" of a data cloud drawn from some unknown probability distribution. Depending on the definition, a principal curve relies on some unknown parameters (number of segments, length, turn. . . ) which have to be properly chosen to recover the shape of the data without interpolating. In the present paper, we consider the principal curve problem from an empirical risk minimization perspective and address the parameter selection issue using the point of view of model selection via penalization. We offer oracle inequalities and implement the proposed approaches to recover the hidden structures in both simulated and real-life data.
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Pré-publication, Document de travail
2011
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https://hal.archives-ouvertes.fr/hal-00565540
Contributeur : Aurélie Fischer <>
Soumis le : lundi 10 octobre 2011 - 14:43:48
Dernière modification le : mardi 11 octobre 2016 - 15:21:05
Document(s) archivé(s) le : mercredi 11 janvier 2012 - 02:25:07

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  • HAL Id : hal-00565540, version 2

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Gérard Biau, Aurélie Fischer. Parameter selection for principal curves. 2011. <hal-00565540v2>

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