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...
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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, gkalgorithm needs added constraint of fuzzy covariance matrix, gkalgorithm 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 gkalgorithms, 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.
The popular fuzzy c-means algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel cluster...
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ISBN:
(纸本)9783037853719
The popular fuzzy c-means algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. However, Gustafson-Kessel clustering algorithm needs added constraint of fuzzy covariance matrix, Gath-Geva clustering algorithm can only be used for the data with multivariate Gaussian distribution. In gk-algorithm, modified Mahalanobis distance with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. In this paper, an improved Normalized Mahalanobis Clustering algorithm Based on FCM by taking a new threshold value and a new convergent process is proposed. The experimental results of real data sets show that our proposed new algorithm has the best performance. Not only replacing the common covariance matrix with the correlation matrix in the objective function in the Normalized Mahalanobis Clustering algorithm Based on FCM, but also replacing the thresholds: D = Sigma Sigma [mu((0))(y)] [(x - a ((0))) (x - a((0)))] > 0.
The popular fuzzy c-means algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel cluster...
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ISBN:
(纸本)9783037854488
The popular fuzzy c-means algorithm based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm were developed to detect non-spherical structural clusters. However, Gustafson-Kessel clustering algorithm needs added constraint of fuzzy covariance matrix, Gath-Geva clustering algorithm can only be used for the data with multivariate Gaussian distribution. In gk-algorithm, modified Mahalanobis distance with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. In this paper, an improved Normalized Supervised Clustering algorithm Based on FCM by taking a new threshold value and a new convergent process is proposed. The experimental results of real data sets show that our proposed new algorithm has the best performance. Not only replacing the common covariance matrix with the correlation matrix in the objective function in the Normalized Supervised Clustering algorithm.
In this paper, we propose a factor weighted fuzzy c-means clustering algorithm. Based on the inverse of a covariance factor, which assesses the collinearity between the centers and samples, this factor takes also into...
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ISBN:
(纸本)9781479956807
In this paper, we propose a factor weighted fuzzy c-means clustering algorithm. Based on the inverse of a covariance factor, which assesses the collinearity between the centers and samples, this factor takes also into account the compactness of the samples within clusters. The proposed clustering algorithm allows to classify spherical and non-spherical structural clusters, contrary to classical fuzzy c-means algorithm that is only adapted for spherical structural clusters. Compared with other algorithms designed for non-spherical structural clusters, such as Gustafson-Kessel, Gath-Geva or adaptive Mahalanobis distance-based fuzzy c-means clustering algorithms, the proposed algorithm gives better numerical results on artificial and real well known data sets. Moreover, this algorithm can be used for high dimensional data, contrary to other algorithms that require the computation of determinants of large matrices. Application on Mid-Infrared spectra acquired on maize root and aerial parts of Miscanthus for the classification of vegetal biomass shows that this algorithm can successfully be applied on high dimensional data.
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