Comparing clusterings and numbers of clusters by aggregation of\n calibrated clustering validity indexes

A key issue in cluster analysis is the choice of an appropriate clustering\nmethod and the determination of the best number of clusters. Different\nclusterings are optimal on the same data set according to different criteria,\nand the choice of such criteria depends on the context and aim of clustering.\nTherefore, researchers need to consider what data analytic characteristics the\nclusters they are aiming at are supposed to have, among others within-cluster\nhomogeneity, between-clusters separation, and stability. Here, a set of\ninternal clustering validity indexes measuring different aspects of clustering\nquality is proposed, including some indexes from the literature. Users can\nchoose the indexes that are relevant in the application at hand. In order to\nmeasure the overall quality of a clustering (for comparing clusterings from\ndifferent methods and/or different numbers of clusters), the index values are\ncalibrated for aggregation. Calibration is relative to a set of random\nclusterings on the same data. Two specific aggregated indexes are proposed and\ncompared with existing indexes on simulated and real data.\n