Discovering meaningful groups in hierarchical cluster analysis. An extension to the multivariate case of a multiple comparison method based on cluster analysis

by Silvia G. Valdano and Julio A. Di Rienzo .

Abstract: In the framework of univariate multiple comparison procedures,there is a hybrid technique joining a hierarchical clustering method with the principles of hypothesis testing. This paper presents an extension to the multivariate case. The new method gives an answer, on the bases of inferencial statistics, to the problem of determining the number of groups in hierarchical cluster analysis. Although, the method was developed as a test for the general hypothesis of equality of population centroids, it performs very well, considering size and power, as a pairwise comparison algorithm. Moreover it avoids the lack of transitivity of classical pairwise comparisons that yields to logical inconsistencies. The method is evaluated and compared, by Monte Carlo simulation, with a partitioning multivariate procedure proposed by Bozdogan and with a multiple comparison algorithm based on the Hotelling’s T2 statistic. An example of grouping provenances of a native South American tree is presented.

Key Words: Data mining, Mahalanobis distance, multivariate multiple comparisons, false discoveries, microarray experiments, unsupervised classification

Authors:
Silvia G Valdano, svaldano@exa.unrc.edu.ar
Julio A. Di Rienzo, dirienzo@agro.uncor.edu

Editor: Bar-Hen Avner, avner@bar-hen.net

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