Adaptative Hausdorff Distances and Dynamic Clustering of Symbolic Interval Data

Francisco de A.T. de Carvalho , Renata M.C.R. de Souza , Marie Chavent (1) , Yves Lechevallier (2, 3)

1 IMB - Institut de Mathématiques de Bordeaux
2 AxIS - Usage-centered design, analysis and improvement of information systems
3 INRIA Rocquencourt

This paper presents a partitional dynamic clustering method for interval data based on adaptive Hausdorff distances. Dynamic clustering algorithms are iterative two-step relocation algorithms involving the construction of the clusters at each iteration and the identification of a suitable representation or prototype (means, axes, probability laws, groups of elements, etc.)f or each cluster by locally optimizing an adequacy criterion that measures the fitting between the clusters and their corresponding representatives. In this paper, each pattern is represented by a vector of intervals. Adaptive Hausdorff distances are the measures used to compare two interval vectors. Adaptive distances at each iteration change for each cluster according to its intra-class structure. The advantage of these adaptive distances is that the clustering algorithm is able to recognize clusters of different shapes and sizes. To evaluate this method, experiments with real and synthetic interval data sets were performed. The evaluation is based on an external cluster validity index (corrected Rand index)in a framework of a Monte Carlo experiment with 100 replications. These experiments showed the usefulness of the proposed method.

Mots clés: adaptive distances.; Symbolic data analysis; dynamic clustering; interval data; Hausdorff distance; adaptive distances

Domaines: Autres [stat.ML]; Apprentissage [cs.LG]

Francisco de A.T. de Carvalho, Renata M.C.R. de Souza, Marie Chavent, Yves Lechevallier. Adaptative Hausdorff Distances and Dynamic Clustering of Symbolic Interval Data. Pattern Recognition Letters, 2006, 27 (3), pp.167-179. ⟨10.1016/j.patrec.2005.08.014⟩. ⟨hal-00200786⟩