Unsupervised Optimal Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Introduction to statistical pattern recognition (2nd ed.)
A Validity Measure for Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Pattern Recognition Letters
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Pattern Recognition Letters
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Fuzzy Models and Algorithms for Pattern Recognition and Image Processing
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IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Computers
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IEEE Transactions on Fuzzy Systems
On cluster validity for the fuzzy c-means model
IEEE Transactions on Fuzzy Systems
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Pattern Recognition Letters
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FS'08 Proceedings of the 9th WSEAS International Conference on Fuzzy Systems
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ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Part II--Advances in Neural Networks
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MLDM '07 Proceedings of the 5th international conference on Machine Learning and Data Mining in Pattern Recognition
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CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
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ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
A stability based validity method for fuzzy clustering
Pattern Recognition
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Pattern Recognition Letters
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Fuzzy Sets and Systems
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ACM Transactions on Knowledge Discovery from Data (TKDD)
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Pattern Recognition Letters
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Pattern Recognition Letters
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Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
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Data Mining and Knowledge Discovery
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Information Sciences: an International Journal
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Neural Computation
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International Journal of Approximate Reasoning
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Cluster validation is a major issue in cluster analysis. Many existing validity indices do not perform well when clusters overlap or there is significant variation in their covariance structure. The contribution of this paper is twofold. First, we propose a new validity index for fuzzy clustering. Second, we present a new approach for the objective evaluation of validity indices and clustering algorithms. Our validity index makes use of the covariance structure of clusters, while the evaluation approach utilizes a new concept of overlap rate that gives a formal measure of the difficulty of distinguishing between overlapping clusters. We have carried out experimental studies using data sets containing clusters of different shapes and densities and various overlap rates, in order to show how validity indices behave when clusters become less and less separable. Finally, the effectiveness of the new validity index is also demonstrated on a number of real-life data sets.