Section: New Results

Adaptive Distances in Clustering Methods

Participants : Marc Csernel, Yves Lechevallier, F.A.T. de Carvalho.

The adaptive dynamic clustering algorithm optimizes a criterion based on a fitting measure between clusters and their prototypes, but the distances used to compare clusters and their prototypes change at each iteration. These distances are not determined absolutely and can be different from one cluster to another. The advantage of these adaptive distances is that the clustering algorithm is able to recognize clusters of different shapes and sizes. The main difference between these algorithms lies in the representation step, which has two stages in the adaptive case. The first stage, where the partition and the distances are fixed and the prototypes are updated, is followed by a second one, where the partition and their corresponding prototypes are fixed and the distances are updated.

We extended these models in order to cluster objects described by interval-valued variables [23] and [22] . Adaptive distances were used to compare a pair of vectors of intervals simultaneously taking into account both the lower and the upper boundaries of the intervals assumed by the interval-valued variables. Moreover, various tools for the interpretation of the partition and cluster of interval-valued data were also presented.

Aditionally, we proposed a clustering algorithm for relational data (dissimilarity data) which is also able to cluster in a polynomial time objects described by set-valued or interval-valued variables constrained by rules [21] . The constraints given by the rules were taking into account through a suitable dissimilarity function.