Possibilistic and Fuzzy c-Means Clustering with Weighted Objects

This paper describes a family of methods of fuzzy clustering handling objects with weights. Weighted objects easily appear when an individual is a representative of several data units. Fuzzy c-means and possibilistic clustering algorithms for weighted objects are proposed. Relationships as well as differences between solutions of possibilistic and fuzzy c-means methods are described. It is also shown that the methods for weighted objects and techniques handling cluster volumes are closely related. A feature in the present approach is a systematic development of a family of algorithms for weighted objects.