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The more sophisticated fuzzy clustering algorithms, like the Gustafson-Kessel algorithm [11] and the fuzzy maximum likelihood estimation (FMLE) algorithm [10] offer the possibility of inducing clusters of ellipsoidal shape and different sizes. The same holds for the EM algorithm for a mixture of Gaussians. However, these additional degrees of freedom often reduce the robustness of the algorithm, thus sometimes rendering their application problematic. In this paper we suggest shape and size regularization methods that handle this problem effectively.

Shape and Size Regularization in Expectation Maximization and Fuzzy Clustering