The multivariate (co)variogram as a spatial weighting function in classification methods

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.