Convergence Theorems of Possibilistic Clustering Algorithms and Generalized Possibilistic Clustering Algorithms

A generalized approach to possibilistic clustering algorithms was proposed in [19], where the memberships are evaluated directly according to the data information using the fuzzy set theory, and the cluster centers are updated via a performance index. The computational experiments based on the generalized possibilistic clustering algorithms in [19] revealed that these clustering algorithms could not provide very stable results when clustering some data sets. As a further investigation on the generalized possibilistic clustering algorithms, this paper discusses the convergence theory in the algorithms and proves that all the generalized possibilistic clustering algorithms convergent to the local minimum of their objective functions.