Fuzzy clustering algorithms and validity indices for distributed data

This chapter presents a unified framework to generalize a number of fuzzy clustering algorithms to handle distributed data in an exact way, i.e., with no approximation of results with respect to their original centralized versions. The same framework allows the exact distribution of relative validity indices used to evaluate the quality of fuzzy clustering solutions. Complexity analyses for each distributed algorithm and index are reported in terms of space, time, and communication aspects. A general procedure to estimate the number of clusters in a non–centralized fashion using the proposed framework is also described. Such a procedure is directly applicable not only to distributed data, but to parallel data processing scenarios as well. Experimental results illustrate the speedup obtained when running algorithms under the proposed framework in multiple cores of a processor, when compared to their traditional, centralized counterparts running in a single core. Additionally, the quality of the results and amount of data transmitted are assessed and compared among different fuzzy clustering algorithms.