M&amp;MFCM: Fuzzy C-means Clustering with Mahalanobis and Minkowski Distance Metrics

Gueorguieva, Natacha; Valova, Iren; Georgiev, George

doi:10.1016/j.procs.2017.09.064

Cited by 26 publications

(16 citation statements)

References 10 publications

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“…In this section, the nonlinear difference equation proposed by Narendra and Parthasarathy [25] is taken as the simulation object, whose expression is formula (20):…”

Section: A Nonlinear Difference Equationmentioning

confidence: 99%

“…This experiment uses cross-validation to test the predictive performance of the proposed method. The random number between [ −2, 2] is taken as the input signal u(k) of the training data and is substituted into formula (20) to obtain 500 training data. Then, we change the input signal to u(k) = sin(2k/25) and plug it into the formula to get 500 sets of test data.…”

Section: A Nonlinear Difference Equationmentioning

confidence: 99%

“…FCM clustering algorithm was used to quickly find out the central functions of two classes of clustering in the image domain in [19]. Mahalanobis and Minkowski metrics are used to replace the usual Euclidean distance in order to enhance the cluster detection capacity of FCM by allowing more accurate detection of arbitrary shapes of clusters for high dimensional datasets in [20]. A clustering method of kernel fuzzy c-regression model based on fuzzy correlation was proposed in [21], which solved the problem of identifying the presupposition parameters of T-S fuzzy model.…”

Section: Introductionmentioning

confidence: 99%

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T-S fuzzy systems optimization identification based on FCM and PSO

Ren

Liu

et al. 2020

EURASIP J. Adv. Signal Process.

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The division of fuzzy space is very important in the identification of premise parameters, and the Gaussian membership function is applied to the premise fuzzy set. However, the two parameters of Gaussian membership function, center and width, are not easy to be determined. In this paper, based on Fuzzy c-means (FCM) and particle swarm optimization (PSO) algorithm, a novel T-S fuzzy model optimal identification method of optimizing two parameters of Gaussian function is presented. Firstly, we use FCM algorithm to determine the Gaussian center for rough adjustment. Then, under the condition that the center of Gaussian function is fixed, the PSO algorithm is used to optimize another adjustable parameter, the width of the Gaussian membership function, to achieve fine-tuning, so as to complete the identification of prerequisite parameters of fuzzy model. In addition, the recursive least squares (RLS) algorithm is used to identify the conclusion parameters. Finally, the effectiveness of this method for T-S fuzzy model identification is verified by simulation examples, and the higher identification accuracy can be obtained by using the novel identification method described compared with other identification methods.

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“…In this section, the nonlinear difference equation proposed by Narendra and Parthasarathy [25] is taken as the simulation object, whose expression is formula (20):…”

Section: A Nonlinear Difference Equationmentioning

confidence: 99%

Section: A Nonlinear Difference Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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T-S fuzzy systems optimization identification based on FCM and PSO

Ren

Liu

et al. 2020

EURASIP J. Adv. Signal Process.

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“…The performance of hard c-means and FCM by using ED and alternative hard c-means and FCM by using new metric norm has been measured by Prasad et al [22]. Gueorguieva et al [23] developed M&MFCM in which they use Mahalanobis and Minkowski distance in place of usual ED. Selvi and Sivasankar [24] introduced an algorithm naming modified cuckoo search (MCS) algorithm that gave an effective recommendation for the optimization of data points.…”

Section: Introductionmentioning

confidence: 99%

Extension of FCM by introducing new distance metric

Kumar

Sharma³

2020

SN Appl. Sci.

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The present article made a significant novel contribution in statistical methodology and dealing with novel and original data analytical clustering algorithm for assigning big data sets into disjoint clusters. The most widely used clustering algorithm is fuzzy c-mean (FCM). But FCM has considerable inconvenience in noisy and outliers data sets because its objective function used Euclidean distance measure for obtaining the communication between data points. It is easily trapped in local optima while the clustering algorithm should be robust and handle these situations. To overcome these problems, this article attempts to generate two distance metrics called advanced metric d AMA and extended metric d EMB that are free from the noisy environment. Then using these distance metrics, two algorithms, advanced metric fuzzy c-mean and extended metric fuzzy c-mean, have been developed for the modification of FCM to achieve the minimization conditions of objective function. These proposed algorithms are more robust than the existing FCM techniques. The efficiency of proposed clustering algorithm is checked by considering numerous examples from different research papers in terms of fitness value, inter-cluster distance and accuracy. The result shows that the proposed algorithms are more robust than the existing algorithms.

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“…In [16] FCM clustering algorithm was used to quickly find out the central functions of two classes of clustering in the image domain. In [17], Mahalanobis and Minkowski used Euclidean distance instead of Euclidean distance to measure Euclidean distance, and improve the clustering detection ability of FCM algorithm by accurately detecting the arbitrary shape of high-dimensional data set. A clustering method of kernel fuzzy c regression model based on fuzzy correlation was proposed in [18], which solved the problem of identifying the presupposition parameters of T-S fuzzy model.…”

Section: Introductionmentioning

confidence: 99%

T-S Fuzzy Systems Optimization Identification Based on FCM and PSO

Zhang

Liu

et al. 2020

Preprint

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Abstract The division of fuzzy space is very important in the identification of premise parameters and the Gaussian membership function is applied to the premise fuzzy set. However, the two parameters of Gaussian membership function, center and width, are not easy to be determined. In this paper, a novel T-S fuzzy model optimal identification method of optimizing two parameters of Gaussian function based on Fuzzy c-means (FCM) and particle swarm optimization (PSO) algorithm is presented. Firstly, we use FCM algorithm to determine the Gaussian center for rough adjustment. Then, under the condition that the center of Gaussian function is fixed, the PSO algorithm is used to optimize another adjustable parameter, the width of the Gaussian membership function, to achieve fine tuning, so as to complete the identification of prerequisite parameters of fuzzy model. In addition, the recursive least squares (RLS) algorithm is used to identify the conclusion parameters. Finally, the effectiveness of this method for T-S fuzzy model identification is verified by simulation examples, and the higher identification accuracy can be obtained by using the novel identification method described compared with other identification methods.

show abstract

M&MFCM: Fuzzy C-means Clustering with Mahalanobis and Minkowski Distance Metrics

Cited by 26 publications

References 10 publications

T-S fuzzy systems optimization identification based on FCM and PSO

T-S fuzzy systems optimization identification based on FCM and PSO

Extension of FCM by introducing new distance metric

T-S Fuzzy Systems Optimization Identification Based on FCM and PSO

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