Automatic validation of hierarchical cluster analysis with application in dialectometry

Successful applications of hierarchical cluster analysis in the area of quantitative linguistics were reported in the pioneering works by Goebl (1982, 1984, 1994). Often the dimensionality of linguistic data is high. Therefore multivariate statistical techniques like cluster analysis can to some degree support the researcher. However there is much room left for heuristics. Cluster analysis methods can be generalized by taking weights of observations into account. Using special weights leads to well-known resampling techniques. Here we offer an automatic validation technique for hierarchical cluster analysis that can be considered as a so-called built-in validation of the number of clusters and of each cluster itself, respectively. Furthermore this built-in validation can be used to find the appropriate cluster analysis model. As an illustration of an application in linguistics, the validation of results of hierarchical clustering based on the adjusted Rand's measure is presented.