Abstract
The multivariate variogram and the multivariate covariogram are used as spatial weighting functions for forming spatially homogeneous groups automatically. The groups are created after either deflating similarities between distant samples with the multivariate covariogram or by inflating dissimilarities between distant samples with the multivariate variogram. These approaches can be seen as generalization of the Oliver and Webster proposal. Two data sets show the efficiency of the two weighting functions when compared to the classical approach which does not take spatial information into account. In one case study, the weighting of similarities by the multivariate covariogram showed more interpretable results than the weighting of dissimilarities by the multivariate variogram.
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Beaumier, M., 1987, Géochimie des Sédiments de Lac de la Région de Schefferville, MB 87-32, M.E.R.Q., 382 p.
Bourgault, G., and Marcotte, D., 1991, Multivariable Variogram and Its Application to the Linear Model of Coregionalization: Math. Geol., v. 23, n. 7, p. 899–928.
David, M., and Dagbert, M., 1974, Lakeview Revisited: Variograms and Correspondence Analysis—New Tools for the Understanding of Geochemical Data, Proc. 5th Exploration Geochemistry Symposium, Elsevier, Amsterdam, p. 163–181.
Dimroth, E., 1978, Labrador Trough Area, Geol. Rep. 193, Min. of Energy and Resources, Quebec, 396 p.
Harff, J., and Davis, J. C., 1990, Regionalization in Geology by Multivariate Classification: Math. Geol., v. 22, p. 573–588.
Journel, A. G., 1988, New Distance Measures; The Route Toward Truly Non-Gaussian Geostatistics: Math. Geol., v. 20, n. 4, p. 459–475.
Lebart, L., 1978, Programme d'Aggrégation avec Contraintes (C.A.H. Contiguïté): Cah. Anal. Données, v. 3, p. 275–287.
Lefkovitch, L. P., 1980, Conditional Clustering: Biometrics, v. 36, p. 43–58.
Legendre, P., 1987, Constraint Clustering,in P. Legendre and L. Legendre (Eds.), Developments in Numerical Ecology, NATO Series, Vol. G 14: Springer-Verlag, Berlin, p. 289–307.
Legendre, P., and Legendre, V., 1984, The Postglacial Dispersal of Freshwater Fishes in the Québec Peninsula: Can. J. Fish. Aquat. Sci., v. 41, p. 1781–1802.
Mackas, D. L., 1984, Spatial Autocorrelation of Plankton Community Composition in a Continental Shelf Ecosystem: Limn. Ocean., v. 29, p. 451–471.
Monestiez, P., 1978, Méthodes de Classification Automatique sous Contraintes Spatiales,in J. M. Legay and R. Tomassone (Eds.), Biométrie et Écologie, Société Française de Biométrie: Paris, p. 367–379.
Morton, D. M., Baird, A. K., and Baird, K. W., 1969, The Lakeview Mountains Pluton, Southern California Batholith, II. Chemical Composition and Variation: Geol. Soc. Am., Bull., v. 80, p. 1553–1564.
Oliver, M. A., and Webster, R., 1989, A Geostatistical Basis for Spatial Weighting in Multivariate Classification: Math. Geol., v. 21, n. 1, p. 15–35.
Ray, D. M., and Berry, B. J. L., 1966, Multivariate Socioeconomic Regionalization: A Pilot Study in Central Canada,in S. Ostry and T. Rymes (Eds.), Papers on Regional Statistical Studies: University of Toronto Press, Toronto, p. 75–130.
Sneath, P. H. A., and Sokal, R. R., 1973, Numerical Taxonomy—The Principles and Practice of Numerical Classification: W. H. Freeman, San Francisco, 573 p.
Sokal, R. R., and Michener, C. D., 1958, A Statistical Method for Evaluating Systematic Relationships: Univ. Kansas Sci. Bull., v. 38, p. 1401–1438.
Young, D. S., 1987, Random Vectors and Spatial Analysis by Geostatistics for Geotechnical Applications: Math. Geol., v. 19, n. 6, p. 467–479.
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Bourgault, G., Marcotte, D. & Legendre, P. The multivariate (co)variogram as a spatial weighting function in classification methods. Math Geol 24, 463–478 (1992). https://doi.org/10.1007/BF00890530
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DOI: https://doi.org/10.1007/BF00890530