Probabilistic clustering via Pareto solutions and significance tests

María Teresa Gallegos and Gunter Ritter ()
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María Teresa Gallegos: University of Passau
Gunter Ritter: University of Passau

Advances in Data Analysis and Classification, 2018, vol. 12, issue 2, No 2, 179-202

Abstract: Abstract The present paper proposes a new strategy for probabilistic (often called model-based) clustering. It is well known that local maxima of mixture likelihoods can be used to partition an underlying data set. However, local maxima are rarely unique. Therefore, it remains to select the reasonable solutions, and in particular the desired one. Credible partitions are usually recognized by separation (and cohesion) of their clusters. We use here the p values provided by the classical tests of Wilks, Hotelling, and Behrens–Fisher to single out those solutions that are well separated by location. It has been shown that reasonable solutions to a clustering problem are related to Pareto points in a plot of scale balance vs. model fit of all local maxima. We briefly review this theory and propose as solutions all well-fitting Pareto points in the set of local maxima separated by location in the above sense. We also design a new iterative, parameter-free cutting plane algorithm for the multivariate Behrens–Fisher problem.

Keywords: Cluster analysis; Probabilistic models; Mixture model; Classification model; Pareto solutions; Behrens–Fisher problem; Hotelling’s $$T^2$$ T 2 statistic; Wilks’ lambda; Primary 62H30; Secondary 62-07 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11634-016-0278-2

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