Partitional fuzzy clustering methods based on adaptive quadratic distances

This paper presents partitional fuzzy clustering methods based on adaptive quadratic distances. The methods presented furnish a fuzzy partition and a prototype for each cluster by optimizing an adequacy criterion based on adaptive quadratic distances. These distances change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another. Moreover, various fuzzy partition and cluster interpretation tools are introduced. Experiments with real and synthetic data sets show the usefulness of these adaptive fuzzy clustering methods and the merit of the fuzzy partition and cluster interpretation tools.