Unifying data units and models in (co-)clustering

Christophe Biernacki () and Alexandre Lourme ()
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Christophe Biernacki: Inria and CNRS
Alexandre Lourme: University of Bordeaux

Advances in Data Analysis and Classification, 2019, vol. 13, issue 1, No 2, 7-31

Abstract: Abstract Statisticians are already aware that any task (exploration, prediction) involving a modeling process is largely dependent on the measurement units for the data, to the extent that it should be impossible to provide a statistical outcome without specifying the couple (unit,model). In this work, this general principle is formalized with a particular focus on model-based clustering and co-clustering in the case of possibly mixed data types (continuous and/or categorical and/or counting features), and this opportunity is used to revisit what the related data units are. Such a formalization allows us to raise three important spots: (i) the couple (unit,model) is not identifiable so that different interpretations unit/model of the same whole modeling process are always possible; (ii) combining different “classical” units with different “classical” models should be an interesting opportunity for a cheap, wide and meaningful expansion of the whole modeling process family designed by the couple (unit,model); (iii) if necessary, this couple, up to the non-identifiability property, could be selected by any traditional model selection criterion. Some experiments on real data sets illustrate in detail practical benefits arising from the previous three spots.

Keywords: Measurement units; Mixed data; Mixture models; Model selection; Non-identifiability; 62H30 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11634-018-0325-2

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