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Communication dans un congrès

Continuity for kriging with moving neighborhood: a penalization approach

Abstract : Solving the kriging equations directly involves the inversion of an n×n covariance matrix C, which becomes numerically intractable when n is too large. Under these circumstances, straightforward kriging of massive datasets is not possible. A common practice is to solve the kriging problem approximately by local approaches that are based on considering only a relatively small number of points that lie close to the target point or block, so as to say in a moving neighborhood. By definition, a moving neighborhood moves with the target. A data point which was within the neighborhood may suddenly be dropped, with a weight jumping from a non-zero to a zero value, in absence of screen effect. The resulting discontinuities of the kriging map are largely undesirable, for instance in digital elevation model. In this work, we propose a method to avoid such discontinuities. It consists in adding a term to the kriging estimation equation that penalizes the weights associated with the most outer data points of the neighborhood. Practically, the penalization relies on a distance function whose value is 0 in most part of the neighborhood and which continuously tends to infinity when approaching its edge. Mechanically, the weights associated with the most outer data points tend to zero as their distance to the edge of the neighborhood gets close to zero. Therefore, the continuity of the resulting kriging map and of the kriging variance map is ensured. General properties of the method are given and illustrated with numerical examples.
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Communication dans un congrès
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https://hal-mines-paristech.archives-ouvertes.fr/hal-00578175
Contributeur : Thomas Romary <>
Soumis le : vendredi 18 mars 2011 - 15:21:22
Dernière modification le : mercredi 14 octobre 2020 - 03:52:25

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  • HAL Id : hal-00578175, version 1

Citation

Thomas Romary, Jacques Rivoirard. Continuity for kriging with moving neighborhood: a penalization approach. IAMG 2010, Aug 2010, Hungary. ⟨hal-00578175⟩

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