Stability in cluster analysis is strongly dependent on the data set, especially on how well separated and how homogeneous the clusters are. In the same clustering, some clusters may be very stable and others may be extremely unstable.The Jaccard coefficient, a similarity measure between sets, is used as a clusterwise measure of cluster stability, which is assessed by the bootstrap distribution of the Jaccard coefficient for every single cluster of a clustering compared to the most similar cluster in the bootstrapped data sets. This can be applied to very general cluster analysis methods.Some alternative resampling methods are investigated as well, namely subsetting, jittering the data points and replacing some data points by artificial noise points. The different methods are compared by means of a simulation study.A data example illustrates the use of the cluster-wise stability assessment to distinguish between meaningful stable and spurious clusters, but it is also shown that clusters are sometimes only stable because of the inflexibility of certain clustering methods.

Summary. Data with mixed-type (metric-ordinal-nominal) variables are typical for social stratification, i.e. partitioning a population into social classes. Approaches to cluster such data are compared, namely a latent class mixture model assuming local independence and dissimilarity-based methods such as k -medoids. The design of an appropriate dissimilarity measure and the estimation of the number of clusters are discussed as well, comparing the Bayesian information criterion with dissimilarity-based criteria. The comparison is based on a philosophy of cluster analysis that connects the problem of a choice of a suitable clustering method closely to the application by considering direct interpretations of the implications of the methodology. The application of this philosophy to economic data from the 2007 US Survey of Consumer Finances demonstrates techniques and decisions required to obtain an interpretable clustering. The clustering is shown to be significantly more structured than a suitable null model. One result is that the data-based strata are not as strongly connected to occupation categories as is often assumed in the literature.

Model-based cluster analysis, Multilayer mixture, Unimodality, Prediction strength, Ridgeline, Dip test, 62H30,

In this paper we introduce three methods for re-scaling data sets aiming at improving the likelihood of clustering validity indexes to return the true number of spherical Gaussian clusters with additional noise features. Our method obtains feature re-scaling factors taking into account the structure of a given data set and the intuitive idea that different features may have different degrees of relevance at different clusters. We experiment with the Silhouette (using squared Euclidean, Manhattan, and the pth power of the Minkowski distance), Dunn???s, Calinski???Harabasz and Hartigan indexes on data sets with spherical Gaussian clusters with and without noise features. We conclude that our methods indeed increase the chances of estimating the true number of clusters in a data set

Biotic element analysis is an alternative to the areas-of-endemism approach for recognizing the presence or absence of vicariance events in a given region. If an ancestral biota was fragmented by vicariance events, biotic elements or clusters of distribution areas should emerge. We propose a statistical test for clustering of distribution areas based on a Monte Carlo simulation with a null model that considers the spatial autocorrelation in the data. The hypothesis tested is that the observed degree of clustering of ranges can be explained by the range size distribution, the varying number of taxa per cell, and the spatial autocorrelation of the occurrences of a taxon alone. A method for the delimitation of biotic elements which uses model-based Gaussian clustering is introduced. We demonstrate our methods and show the importance of grid size by means of a case study, an analysis of the distribution patterns of southern African species of the weevil genus Scobius. The example highlights the difficulties in delimiting areas of endemism if dispersal has occurred and illustrates the advantages of the biotic element approach.