Probabilistic Aspects in Cluster Analysis

The historical evolution shows a surprising trend from an algorithmic, heuristic and applications oriented point of view to a more basic, theory oriented investigation of the structural, mathematical and statistical properties of clustering methods.

Abstract

Cluster analysis provides methods and algorithms for partitioning a set of objects O = 1,…, n (or data vectors x1,…, xn ∈ R p ) into a suitable number of classes C1,…,Cm ⊆ O such that these classes are homogeneous and each of them comprizes only objects which are'similar' in some sense. The historical evolution shows a surprising trend from an algorithmic, heuristic and applications oriented point of view (Sokal/Sneath 1963) to a more basic, theory oriented investigation of the structural, mathematical and statistical properties of clustering methods. Nowadays, the questions to be answered are of the type'How many clusters are there ?','Is there a classification structure ?','Is the calculated classification adequate ?','Which are the strongest clusters ?' etc.