Data analysis with fuzzy clustering methods

An encompassing, self-contained introduction to the foundations of the broad field of fuzzy clustering is presented. The fuzzy cluster partitions are introduced with special emphasis on the interpretation of the two most encountered types of gradual cluster assignments: the fuzzy and the possibilistic membership degrees. A systematic overview of present fuzzy clustering methods is provided, highlighting the underlying ideas of the different approaches. The class of objective function-based methods, the family of alternating cluster estimation algorithms, and the fuzzy maximum likelihood estimation scheme are discussed. The latter is a fuzzy relative of the well-known expectation maximization algorithm and it is compared to its counterpart in statistical clustering. Related issues are considered, concluding with references to selected developments in the area.