This paper addresses three major issues associated with conventional partitional clustering, namely, sensitivity to initialization, difficulty in determining the number of clusters, and sensitivity to noise and outliers. The proposed Robust Competitive Agglomeration (RCA) algorithm starts with a large number of clusters to reduce the sensitivity to initialization, and determines the actual number of clusters by a process of competitive agglomeration. Noise immunity is achieved by incorporating concepts from robust statistics into the algorithm. RCA assigns two different sets of weights for each data point: the first set of constrained weights represents degrees of sharing, and is used to create a competitive environment and to generate a fuzzy partition of the data set. The second set corresponds to robust weights, and is used to obtain robust estimates of the cluster prototypes. By choosing an appropriate distance measure in the objective function, RCA can be used to find an unknown number of clusters of various shapes in noisy data sets, as well as to fit an unknown number of parametric models simultaneously. Several examples, such as clustering/mixture decomposition, line/plane fitting, segmentation of range images, and estimation of motion parameters of multiple objects, are shown.

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The fuzzy c spherical shells (FCSS) algorithm is specially designed to search for clusters that can be described by circular arcs or, generally, by shells of hyperspheres. A new approach to the FCSS algorithm is presented. This algorithm is computationally and implementationally simpler than other clustering algorithms that have been suggested for this purpose. An unsupervised algorithm which automatically finds the optimum number of clusters is not known. It uses a cluster validity measure to identify good clusters, merges all compatible clusters, and eliminates spurious clusters to achieve the final results. Experimental results on several data sets are presented.