L- and V-curves for optimal smoothing. (February 2015)

• Record Type: Journal Article
• Authors: Frasso, Gianluca; Eilers, Paul HC
• Is Part Of: Statistical modelling. Volume 15:Number 1(2015)
• Page Start: 91
• Page End: 111
• Publication Date: 2015-02
• Subjects: Cross-validation -- L-curve -- V-curve -- Whittaker and P-spline smoothers; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X14549288
• Languages: English
• ISSNs: 1471-082X

Abstract

The L-curve is a tool for the selection of the regularization parameter in ill-posed inverse problems. It is a parametric plot of the size of the residuals vs that of the penalty. The corner of the L indicates the right amount of regularization. In the context of smoothing the L-curve is easy to compute and works surprisingly well, even for data with correlated noise. We present the theoretical background and applications to real data together with an alternative criterion for finding the corner automatically. We introduce as simplification, the V-curve, which replaces finding the corner of the L-curve by locating a minimum.