Probability models and hypotheses testing in partitioning cluster analysis

In: Ph. Arabie, L. Hubert, G. De Soete (eds.): Clustering and classification. World Science Publishers, River Edge/NJ, 1996, 377-453.

The paper surveys the recent mathematical, statistical and empirical results on probabilistic aspects and testing methods in cluster analysis, emphasizing the partitioning approach. The titles of the sections are:

1. Probability Models in Cluster Analysis
2. Probabilistic Clustering Models in R^p
3. Clustering Criteria for the Fixed-partition Model
4. The Asymptotic Behavior of Optimization-based Clustering
5. Mixture Models for Clustering, Random-partition Model
6. Testing for Uniformity, Unimodality, and Multimodality
7. Test Statistics Based on Classification Models
8. Determining the Unknown Number of Classes
9. Conclusions

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