Fuzzy clustering of non-convex patterns using global optimization
Beliakov, Gleb 2001, Fuzzy clustering of non-convex patterns using global optimization, in Meeting the grand challenge : machines that serve people : [proceedings of] the 10th IEEE International Conference on Fuzzy Systems, December 2001, 2-5 December, the University of Melbourne, Australia, IEEE, Melbourne, Vic, pp. 220-223.
This paper discusses various extensions of the classical within-group sum of squared errors functional, routinely used as the clustering criterion. Fuzzy c-means algorithm is extended to the case when clusters have irregular shapes, by representing the clusters with more than one prototype. The resulting minimization problem is non-convex and non-smooth. A recently developed cutting angle method of global optimization is applied to this difficult problem
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