Parameter selection for principal curves - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue IEEE Transactions on Information Theory Année : 2012

Parameter selection for principal curves

Résumé

Principal curves are nonlinear generalizations of the notion of first principal component. Roughly, a principal curve is a parameterized curve in R-d 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, etc.) which have to be properly chosen to recover the shape of the data without interpolating. In this 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 approach to recover the hidden structures in both simulated and real-life data.

Dates et versions

hal-00704941 , version 1 (06-06-2012)

Identifiants

Citer

Gérard Biau, A. Fischer. Parameter selection for principal curves. IEEE Transactions on Information Theory, 2012, 58 (3), pp.1924-1939. ⟨10.1109/TIT.2011.2173157⟩. ⟨hal-00704941⟩
79 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More