Fuzzy K-means clustering algorithms for interval-valued data based on adaptive quadratic distances

This paper presents partitioning fuzzy K-means clustering models for interval-valued data based on suitable adaptive quadratic distances. These models furnish a fuzzy partition and a prototype for each cluster by optimizing an adequacy criterion that measures the fit between the fuzzy clusters and their representatives. These adaptive quadratic distances change at each algorithm iteration and can be either the same for all clusters or different from one cluster to another. Moreover, additional interpretation tools for individual fuzzy clusters of interval-valued data, suitable to these fuzzy clustering models, are also presented. Experiments with some interval-valued data sets demonstrate the usefulness of these fuzzy clustering models and the merit of the individual fuzzy cluster interpretation tools.