Data-Driven Extrapolation Via Feature Augmentation Based on Variably Scaled Thin Plate Splines

Thin-Plate Splines

2 The Calculus of Variations 2 2.1 Functionals of f and f ′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Functionals of f , f ′, and f ′′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Cubic Splines and Green’s Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Euler-Lagrange Equations for Multi...

Thin plate regression splines

I discuss the production of low rank smoothers for d ≥ 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thinplate spline smoothing problem, and are optimal in the sense that the truncation is designed to result in the minimum possible pe...

Finite Element Thin Plate Splines

Finite Element Thin Plate Splines for Data Mining Applications

Thin plate splines have been used successfully to model curves and surfaces. A new application is in data mining where they are used to model interaction terms. These interaction splines break the \curse of dimensionality" by reducing the high-dimensional nonparametric regression problem to the determination of a set of interdependent surfaces. However, the determination of the corresponding th...

Fingerprint Mosaicing Using Thin Plate Splines

We discuss a fingerprint mosaicing scheme to construct a composite fingerprint image using multiple impressions of the same finger. The composite image is expected to contain more information (e.g., minutiae) compared to the individual impressions thereby improving matching accuracy. The novelty of the proposed algorithm lies in its ability to account for the elastic deformation present in cons...