Selecting the length of a principal curve within a Gaussian model

Aurélie Fischer (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

Principal curves are parameterized curves passing "through the middle" of a data cloud. These objects constitute a way of generalization of the notion of first principal component in Principal Component Analysis. Several definitions of principal curve have been proposed, one of which can be expressed as a least-square minimization problem. In the present paper, adopting this definition, we study a Gaussian model selection method for choosing the length of the principal curve, in order to avoid interpolation, and obtain a related oracle-type inequality. The proposed method is practically implemented and illustrated on cartography problems.

Mots clés: principal curves; model selection; oracle inequality; slope heuristics.; slope heuristics

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Aurélie Fischer. Selecting the length of a principal curve within a Gaussian model. 2012. ⟨hal-00712097⟩