Convergence theory for fuzzy c-means: counterexamples and repairs
IEEE Transactions on Systems, Man and Cybernetics
Characterization and detection of noise in clustering
Pattern Recognition Letters
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Foundations of Neuro-Fuzzy Systems
Foundations of Neuro-Fuzzy Systems
Foundations of Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Fuzzy c-means improvement using relaxed constraints support vector machines
Applied Soft Computing
Information Technology and Management
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The well-known fuzzy c-means algorithm is an objective function based fuzzy clustering technique that extends the classical k-means method to fuzzy partitions. By replacing the Euclidean distance in the objective function other cluster shapes than the simple (hyper-)spheres of the fuzzy c-means algorithm can be detected, for instance ellipsoids, lines or shells of circles and ellipses. We propose a modified distance function that is based on the dot product and allows to detect a new kind of cluster shape and also lines and (hyper-)planes.