A Probability theory of hierarchic clustering using random dendrograms

Abstract

It is widely recognized that a major, current problem in cluster analysis is that of validating results. This paper looks at one possible approach to the validation of results. It considers the structure of (unlabelled) dendrograms and proposes a model of random dendrograms. Algorithms for calculating the probability distribution of a coefficient of structure of a dendrogram are discussed, —both by enumeration of distinct dendrograms, and by Monte Carlo generation of dendrograms

Keywords:

• Cluster analysis
• statistical inference
• hierarchic structure
• unlabelled dendrogram
• enumeration
• Monte Carlo method