Spatial orthogonality of the principal components computed from coregionalized variables |
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| Authors: | P Goovaerts |
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| Institution: | (1) Unité de Biométrie, Université Catholique de Louvain, Place Croix du Sud 2 Bte 16, B-1348 Louvain-la-Neuve, Belgique;(2) Present address: Department of Applied Earth Science, Stanford University, 94305 Stanford, California |
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| Abstract: | Within the frame of the linear model of coregionalization, this paper sets up equations relating the variogram matrix of the principal components extracted from the variance-covariance matrix to the diagonal variogram matrices of the regionalized factors. The spatial orthogonality of the principal components is investigated in three situations: the intrinsic correlation, two basic structures with independent nugget components, three basic structures with independent nugget components and uncorrelated subsets of variables. Two examples point out that the correlation between the principal components may be nonnegligible at short distances, especially if the correlation structure changes according to the spatial scale considered. For one of the two case studies, an orthogonal varimax rotation of the first principal components is found to greatly reduce the spatial correlation between some of them. |
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| Keywords: | variogram matrix linear model of coregionalization principal component analysis intrinsic correlation orthogonal rotation |
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