Convex fuzzy k-medoids clustering

Abstract K-medoids clustering is among the most popular methods for cluster analysis despite its use requiring several assumptions about the nature of the latent clusters. In this paper, we introduce the Convex Fuzzy k-Medoids (CFKM) model, which not only relaxes the assumption that objects must be assigned entirely to one and only one medoid, but also that medoids must be assigned entirely to one and only one cluster. The resulting model is convex, thus its resolution is completely robust to initialization. To illustrate the usefulness of the CFKM model, we compare it with two fuzzy k-medoids clustering models: the Fuzzy k-Medoids (FKM) and the Fuzzy Clustering with Multi-Medoids (FMMdd), both solved approximately by heuristics because of their hard computational complexity. Our experiments with both synthetic and real-world data as well as a user survey reveal that the model is not only more robust to the choice hyperparameters of the fuzzy clustering task, but also that it can uniquely discover important aspects of data inherently fuzzy in nature.