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A Validity Measure for Fuzzy Clustering
August 1991 (vol. 13 no. 8)
pp. 841-847

The authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c-partitions without assumptions as to the number of substructures inherent in the data. This function depends on the data set, geometric distance measure, distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used. The function is mathematically justified via its relationship to a well-defined hard clustering validity function, the separation index for which the condition of uniqueness has already been established. The performance of this validity function compares favorably to that of several others. The application of this validity function to color image segmentation in a computer color vision system for recognition of IC wafer defects which are otherwise impossible to detect using gray-scale image processing is discussed.

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Index Terms:
fuzzy clustering; fuzzy validity criterion; validity function; fuzzy c-partitions; geometric distance measure; cluster centroids; separation index; uniqueness; color image segmentation; computer color vision system; IC wafer defects; fuzzy set theory; minimisation; pattern recognition
X.L. Xie, G. Beni, "A Validity Measure for Fuzzy Clustering," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 8, pp. 841-847, Aug. 1991, doi:10.1109/34.85677
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