A fuzzy weighted clustering method for symbolic interval data

This article presents a new fuzzy clustering algorithm for interval-valued symbolic variables. We also make a comparative study with other fuzzy weighted clustering methods for interval-valued symbolic data. These adressed approaches are generalizations of the fuzzy c-means clustering for interval-valued symbolic data (IFCM) algorithm except that their distances are weighted by a parameter that measures the influence of individual variables on detected clusters. These methods are objective function-based techniques, so they optimize an adequacy criterion based on some distance for symbolic data. They include the calculation of these weights in the representation step so the distances change at each algorithm´s iteration. The parameters differ from one cluster to another. Through these algorithms we can obtain clusters with different shapes and sizes overcoming some drawbacks of IFCM. We also show how the parameters are influenced by the variance of each variable and the impact of its calculation using an additive and a multiplicative constraint on the clusters obtained. Experiments with real and synthetic symbolic data sets shows the efficiency of these methods for each situation.