Sample Size Requirements for Stable Clustering of Free Partition Sorting Data

Abstract

Convergence rates of cluster analysis results are studied for six sets of partition sorting data. Hierarchical cluster analysis, fuzzy cluster analysis, k-medoids clustering and four variants of the consensus clustering method are covered. The six data sets are kinship terms, colour plates, drug data, consultancy Web site items, social groups and prenatal tests. Convergence rates depend on the number of clusters extracted, on the clustering method and on the domain. For domains of 25 items or more, cluster analysis results identical to the final result were most consistently obtained using the third method of Gordon and Vichi (2001). Example evaluations are given for the most stable numbers of clusters for five sets of partition sorting using the method of Gordon and Vichi. The interpretations resemble previously published interpretations of results obtained from non-partitioning statistical methods.