Section: New Results

Keywords : unsupervised clustering, distances table.

Divisive clustering with constraints

Participant : Yves Lechevallier.

DIVCLUS-T is a divisive and monothetic hierarchical clustering method which proceeds by optimization of a polythetic criterion [74] . The bipartitional algorithm and the choice of the cluster to be split are based on the minimization of the within-cluster inertia. The complete enumeration of all possible bipartitions is avoided by using the same monothetic approach as Breiman et al. (1984) who proposed, and used, binary questions in a recursive partitional process, CART, in the context of discrimination and regression. In the context of clustering, there are no predictors and no response variable.

We propose an extension of DIVCLUS-T, called C-DIVCLUS-T which is able to take contiguity constraints into account. Because the new criterion defined to include these constraints is a distance-based criterion, C-DIVCLUS-T will be able to deal with complex data. In order to avoid the problem pointed out below concerning the definition of binary questions for complex data, we impose to the variables used in the the binary questions, to be classical. The variables used in the calculation of the distance-based criterion can however have complex descriptions.

The method [23] and [41] proposed has the specificity to be monothetic and its main advantage is then the simple and natural interpretation of the dendrogram and the clusters of the hierarchy. Of course these monothetic descriptions are also constraints which may deteriorate the quality of the divisions.