Measuring the Power of Hierarchical Cluster Analysis

Abstract

The concept of power for monotone invariant clustering procedures is developed via the possible partitions of objects at each iteration level in the obtained hierarchy. At a given level, the probability of rejecting the randomness hypothesis is obtained empirically for the possible types of partitions of the n objects employed. The results indicate that the power of a particular hierarchical clustering procedure is a function of the type of partition. The additional problem of estimating a “true” partition at a certain level of a hierarchy is discussed briefly.