Robust and Fuzzy Spherical Clustering by a Penalty Parameter Approach

A spherical clustering algorithm that provides robustness against noise and outliers is proposed. It is formulated as a constrained nonlinear optimization problem inspired by the idea of using minimum radii spheres of support vector clustering. An augmented cost function obtained by the penalty parameter approach is minimized by a stable coupled gradient network. Minimizing the first term in the cost forces spheres to include all the data while the second term is responsible for having small radii spheres. The third term added to the cost via a time-varying penalty parameter forces each datum to be assigned to the clusters with unity-sum membership values. It has been observed from the applications performed on the artificial and IRIS data sets that suitably chosen penalty parameters create tradeoffs among the cost terms providing fuzziness and robustness.