Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods

Abstract

Two robustness criteria are presented that are applicable to general clustering methods. Robustness and stability in cluster analysis are not only data dependent, but even cluster dependent. Robustness is in the present paper defined as a property of not only the clustering method, but also of every individual cluster in a data set. The main principles are: (a) dissimilarity measurement of an original cluster with the most similar cluster in the induced clustering obtained by adding data points, (b) the dissolution point, which is an adaptation of the breakdown point concept to single clusters, (c) isolation robustness: given a clustering method, is it possible to join, by addition of g points, arbitrarily well separated clusters? Results are derived for k-means, k-medoids ( k estimated by average silhouette width), trimmed k-means, mixture models (with and without noise component, with and without estimation of the number of clusters by BIC), single and complete linkage.