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Probabilistic Aspects in Cluster Analysis

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Conceptual and Numerical Analysis of Data

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.

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  1. Institut für Statistik und Wirtschaftsmathematik, Technical University Aachen, Germany

    H. H. Bock

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  1. Lehrstuhl für Mathematische Methoden, Wirtschaftswissenschaften Universität Augsburg, Memminger Straße 14, D-8900, Augsburg, Germany

    Otto Optiz

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Bock, H.H. (1989). Probabilistic Aspects in Cluster Analysis. In: Optiz, O. (eds) Conceptual and Numerical Analysis of Data. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75040-3_2

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