The Concentration centroid Minimum Distance Clustering Criterion

Abstract

Building homogenous classes is one of the main goals in clustering. Homogeneity can be measured by the intra-class variance (Bock, 1998). Especially in erosion projects but in other applications as well the separation between the built classes is as important as the homogeneity of the classes. Special clustering methods can be used to reach this aim, for instance the Maximum Linkage Algorithm (Zerbst, 2001) or the Advanced Maximum Linkage Algorithm (Tschiersch, 2002). To judge the separation quality of such clusterings, the shortest distances between all centroids is considered. Zerbst (2001) shows that the arithmetic mean over all distances isn’t good enough for judging selectivity. Therefore the concentration centroid minimum distance criterion is proposed in this paper. This criterion is based on the ratio of weighted symmetric mean over the minimal distances and the Gini coefficient over the minimal distances. It also judges the class separation independent of the underlying data situation.