Variable-geometry clustering and its optimization

Clustering is often viewed as a synonym of techniques used to reveal the structure in data. The inherent geometrical diversity of data is a strong motivating factor to search for geometrically flexible clusters design supported by the clustering algorithms. In this study, we introduce a concept of geometrically variable fuzzy clustering (making use of Fuzzy C-Means, FCM), in which the fuzzification coefficients are associated with individual clusters thus endowing them with significant geometric flexibility. We introduce a hybrid optimization environment in which both global and local optimization mechanisms are engaged. The global optimization is supported by evolutionary computing (and particle swarm optimization, PSO, in particular) whereas the local optimization is realized by adopting some modified iterative schemes encountered in FCM. We show that this hybrid vehicle of optimization is of interest when dealing with comprehensive fitness functions which quantify a general view at the results of clustering (such as e.g., the one expressed by cluster validity indexes or the one articulating the mapping- reconstruction capabilities of the clusters).