Possibilistic and probabilistic fuzzy clustering: unification within the framework of the non-extensive thermostatistics

摘要: Fuzzy clustering algorithms are becoming the major technique in cluster analysis. In this paper, we consider fuzzy based on objective functions. They can be divided into two categories: possibilistic and probabilistic approaches leading to different function families depending conditions required state that clusters a c-partition of input data. Recently, have presented Menard Eboueya (Fuzzy Sets Systems, 27, published) an axiomatic derivation Possibilistic Maximum Entropy Inference (MEI) approaches, upon unifying principle physics, extreme physical information (EPI) defined by Frieden (Physics from Fisher information, A unification, Cambridge University Press, Cambridge, 1999). Here, using same formalism, explicitly give new criterion order provide theoretical justification functions, constraint terms, membership functions weighting exponent m used clustering. Moreover, propose unified framework including procedures. This approach is inspired work Plastino Miller 235, 577) extending extremal non-extensive thermostatistics. Then, show how, with help EPI, one extensions FcM algorithms.