Enhancing the selection of a model-based clustering with external categorical variables

• Published in: Advances in data analysis and classification Vol. 9; no. 2; pp. 177 - 196
• Main Authors: Baudry, Jean-Patrick, Cardoso, Margarida, Celeux, Gilles, Amorim, Maria José, Ferreira, Ana Sousa
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2015
• Subjects: Chemistry and Earth Sciences; Computer Science; Data Mining and Knowledge Discovery; Economics; Finance; Health Sciences; Humanities; Insurance; Law; Management; Mathematics and Statistics; Medicine; Physics; Regular Article; Statistical Theory and Methods; Statistics; Statistics for Business; Statistics for Engineering; Statistics for Life Sciences; Statistics for Social Sciences; ICL; Mixed type variables clustering; Number of clusters; Mixture models; Model-based clustering; Penalised criteria; 62H30; Categorical variables; BIC
• ISSN: 1862-5347; 1862-5355
• DOI: 10.1007/s11634-014-0177-3

In cluster analysis, it can be useful to interpret the partition built from the data in the light of external categorical variables which are not directly involved to cluster the data. An approach is proposed in the model-based clustering context to select a number of clusters which both fits the data well and takes advantage of the potential illustrative ability of the external variables. This approach makes use of the integrated joint likelihood of the data and the partitions at hand, namely the model-based partition and the partitions associated to the external variables. It is noteworthy that each mixture model is fitted by the maximum likelihood methodology to the data, excluding the external variables which are used to select a relevant mixture model only. Numerical experiments illustrate the promising behaviour of the derived criterion.