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Fuzzy C-Means Algorithm Based on Common Mahalanobis Distances
Hsiang-Chuan Liu, Jeng-MingYih, Wen-Chih Lin and Der-Bang Wu

Some of the well-known fuzzy clustering algorithms are based on Euclidean distance function, which can only be used to detect spherical structural clusters. Gustafson-Kessel (GK) clustering algorithm and Gath Geva (GG) clustering algorithm were developed to detect non-spherical structural clusters. However, GK algorithm needs added constraint of fuzzy covariance matrix, GK algorithm can only be used for the data with multivariate Gaussian distribution. A Fuzzy C-Means algorithm based on Mahalanobis distance (FCM-M) was proposed by our previous work to improve those limitations of GG and GK algorithms, but it is not stable enough when some of its covariance matrices are not equal. In this paper, A improved Fuzzy C-Means algorithm based on a Common Mahalanobis distance (FCM-CM) is proposed The experimental results of three real data sets show that the performance of our proposed FCM-CM algorithm is better than those of the FCM, GG, GK and FCM-M algorithms.

Keywords: Fuzzy C-Means algorithm, GK-algorithm, GG-algorithm, FCM-M algorithm, FCM-CM algorithm.

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