Fuzzy Clustering: A Historical Perspective

Fuzzy sets emerged in 1965 in a paper by Lotfi Zadeh. In 1969 Ruspini published a seminal paper that has become the basis of most fuzzy clustering algorithms. His ideas established the underlying structure for fuzzy partitioning, and also described and exemplified the first algorithm for accomplishing it. Bezdek developed the general case of the fuzzy c-means model in 1973. Many branches of this tree grew from 1969 to 1993. Then another watershed paper in fuzzy clustering appeared: Krishnapuram and Keller?s work on possibilistic clustering. This tree has also developed many branches, and together, these two topics comprise two thirds (of the conceptual field) of soft clustering (the other third belongs to probabilistic clustering in its many guises). Another important class of fuzzy and possibilistic methods, known as generalized clustering, were later developed, based on the idea of stressing the internal nature of clusters rather than solely on metric notions or on the sharing of some significant traits. This article reviews some of the key highlights of fuzzy and possibilistic clustering. This is not a comprehensive survey: that would require an article the size of an encyclopedia and an army of well-informed authors. The best we can do here is to give readers a small glimpse of the overall reach and span of Zadeh's idea in the vast jungle that is fuzzy cluster analysis.