Fuzzy C-Mean Algorithm Based on Mahalanobis Distances and Better Initial Values

Liu, Hsiang-Chuan; Yih, Jeng-Ming; Liu, Shin-Wu

doi:10.1142/9789812709677_0199

Cited by 30 publications

(32 citation statements)

References 1 publication

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“…Gath and Geva (1989) [9] assumed that the normal distribution with expected value and covariance matrix is chosen for generating a datum with prior probability, satisfying…”

Section: Gg Algorithmmentioning

confidence: 99%

“…The Fuzzy C-Means algorithm based on adaptive Mahalanobis distances, common Mahalanobis distance and standardized Mahalanobis distance, respectively (FCM-M and FCM-CM), [8][9][10][11][12]13] were proposed, and then, the fuzzy covariance matrices in the Mahalanobis distance can be directly derived by minimizing the objective function. In our three previous works, to add a regulating factor of Each covariance matrix to each class in the objective function, and deleted the constraint of the determinants of covariance matrices in the GK algorithm, the Fuzzy C-Means algorithm based on adaptive Mahalanobis distances, common Mahalanobis distance and standardized Mahalanobis distance, respectively (FCM-M and FCM-CM), [8][9][10][11][12]13] were proposed, and then, the fuzzy covariance matrices in the Mahalanobis distance can be directly derived by minimizing the objective function.…”

Section: Introductionmentioning

confidence: 99%

“…In our three previous works, to add a regulating factor of Each covariance matrix to each class in the objective function, and deleted the constraint of the determinants of covariance matrices in the GK algorithm, the Fuzzy C-Means algorithm based on adaptive Mahalanobis distances, common Mahalanobis distance and standardized Mahalanobis distance, respectively (FCM-M and FCM-CM), [8][9][10][11][12]13] were proposed, and then, the fuzzy covariance matrices in the Mahalanobis distance can be directly derived by minimizing the objective function.…”

Section: Introductionmentioning

confidence: 99%

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Clustering Accuracies on Concepts of Mathematics

Yih¹

2017

dtetr

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Abstract. Fuzzy c-means algorithm (FCM) 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. 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.

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“…Gath and Geva (1989) [9] assumed that the normal distribution with expected value and covariance matrix is chosen for generating a datum with prior probability, satisfying…”

Section: Gg Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Clustering Accuracies on Concepts of Mathematics

Yih¹

2017

dtetr

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show abstract

“…An improved implementation (to be investigated in the future) would include a different covariance matrix for each class and thus require iterative updates of based on the class membership at each iteration [11].…”

Section: Modified Fcm For Healthy and Abnormal Tissue Segmentationmentioning

confidence: 99%

Fuzzy Multi-channel Clustering with Individualized Spatial Priors for Segmenting Brain Lesions and Infarcts

Zacharaki

Erus

Bezerianos

et al. 2012

IFIP Advances in Information and Communication Technology

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Abstract. Quantitative analysis of brain lesions and ischemic infarcts is becoming very important due to their association with cardiovascular disease and normal aging. In this paper, we present a semi-supervised segmentation methodology that detects and classifies cerebrovascular disease in multi-channel magnetic resonance (MR) images. The method combines intensity based fuzzy c-means (FCM) segmentation with spatial probability maps calculated from a normative set of images from healthy individuals. Unlike common FCM-based methods which segment only healthy tissue, we have extended the fuzzy segmentation to include patient-specific spatial priors for both pathological conditions (lesions and infarcts). These priors are calculated by estimating the statistical voxel-wise variation of the healthy anatomy, and identifying abnormalities as deviations from normality. False detection is reduced by knowledgebased rules. Assessment on a population of 47 patients from different imaging sites illustrates the potential of the proposed method in segmenting both hyperintense lesions and necrotic infarcts.

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“…A regulating factor of the covariance matrix is added to each class in the objective function, and the constraint of the determinant of the covariance matrices defined in the G-K algorithm is removed. Furthermore, the FCM-AM algorithms included two algorithms, FCM-M and FCM-CM, proposed by our previous works (Hsiang-Chuan Liu, Jeng-Ming Yih, Shin-Wu Liu, 2007). …”

Section: Introductionmentioning

confidence: 99%

Clustering with fuzzy supervised algorithm

2017

Self Cite

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Abstract. 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. A Fuzzy C-Means algorithm based on Mahalanobis distance (FCM-M) was proposed 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, an improved 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 Supervised Clustering Algorithm.

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Fuzzy C-Mean Algorithm Based on Mahalanobis Distances and Better Initial Values

Cited by 30 publications

References 1 publication

Clustering Accuracies on Concepts of Mathematics

Clustering Accuracies on Concepts of Mathematics

Fuzzy Multi-channel Clustering with Individualized Spatial Priors for Segmenting Brain Lesions and Infarcts

Clustering with fuzzy supervised algorithm

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