A generalization of inverse distance weighting and an equivalence relationship to noise-free Gaussian process interpolation via Riesz representation theorem |
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Authors: | Wim De Mulder Geert Molenberghs Geert Verbeke |
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Affiliation: | 1. I-BioStat, KU Leuven, Leuven, Belgium.;2. I-BioStat, Universiteit Hasselt, Hasselt, Belgium. |
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Abstract: | In this paper, we show the relationship between two seemingly unrelated approximation techniques. On the one hand, a certain class of Gaussian process-based interpolation methods, and on the other hand inverse distance weighting, which has been developed in the context of spatial analysis where there is often a need for interpolating from irregularly spaced data to produce a continuous surface. We develop a generalization of inverse distance weighting and show that it is equivalent to the approximation provided by the class of Gaussian process-based interpolation methods. The equivalence is established via an elegant application of Riesz representation theorem concerning the dual of a Hilbert space. It is thus demonstrated how a classical theorem in linear algebra connects two disparate domains. |
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Keywords: | Riesz representation theorem Gaussian process inverse distance weighting interpolation kriging |
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