Improved Possibilistic C-Means Clustering Algorithms

Zhang, Jiangshe; Leung, Yiu-Wing

doi:10.1109/tfuzz.2004.825079

Cited by 153 publications

(75 citation statements)

References 12 publications

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“…Another improved version of the PCM algorithm that combines fuzzy and possibilistic memberships is proposed in [20]. To be able to keep the fuzzy approach and use a possibilistic partition, the authors replace the similarity criteria in the FCM distortion function by the distortion function defined in the PCM algorithm, obtaining the following distortion function to be minimized:…”

Section: Improved Possibilistic C-means (Ipcm)mentioning

confidence: 99%

“…This new algorithm uses a possibilistic partition and a fuzzy partition, combining both approaches as it was done in IPCM [20]. The objective function to be minimized is defined as:…”

Section: Improved Possibilistic Cfa (Ipcfa)mentioning

confidence: 99%

“…Within the modifications of the original algorithm, a fuzzy partition of the data was introduced. There are several kinds of possibilistic partitions that can improve the performance of the fuzzy partition as it has been shown in [20,10,12]. In this paper, the fuzzy partition of the ICFA algorithm will be replaced by the several possibilistic approaches found in the literature and a comparative analysis will be made for each of them.…”

Section: Introductionmentioning

confidence: 99%

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Studying possibility in a clustering algorithm for RBFNN design for function approximation

Guillén¹,

Pomares

Rojas

et al. 2007

Neural Comput & Applic

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The function approximation problem has been tackled many times in the literature by using Radial Basis Function Neural Networks (RBFNNs). In the design of these neural networks there are several stages where, the most critical stage is the initialization of the centers of each RBF since the rest of the steps to design the RBFNN strongly depend on it. The Improved Clustering for Function Approximation (ICFA) algorithm was recently introduced and proved successful for the function approximation problem. In the ICFA algorithm a fuzzy partition of the input data is performed but, a fuzzy partition can behave inadequately in noise conditions. Possibilistic and mixed approaches, combining fuzzy and possibilistic partitions, were developed in order to improve the performance of a fuzzy partition. In this paper, a study of the influence of replacing the fuzzy partition used in the ICFA algorithm with the possibilistic and the fuzzypossibilistic partitions will be done. A comparative analysis of each kind of partition will be performed in order to see if the possibilistic approach can improve the performance of the ICFA algorithm both in normal and in noise conditions. The results will show how the employment of a mixed approach combining fuzzy and possibilistic approach can lead to improve the results when designing RBFNNs.

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Section: Improved Possibilistic C-means (Ipcm)mentioning

confidence: 99%

“…This new algorithm uses a possibilistic partition and a fuzzy partition, combining both approaches as it was done in IPCM [20]. The objective function to be minimized is defined as:…”

Section: Improved Possibilistic Cfa (Ipcfa)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Studying possibility in a clustering algorithm for RBFNN design for function approximation

Guillén¹,

Pomares

Rojas

et al. 2007

Neural Comput & Applic

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“…In 2004, Jiang-She Zhang and Yiu-W ing Leung [13] changed the possibilistic approach given in [3] to overcome its drawbacks. The main idea was to integrate a fuzzy approach into their objective function, so that the improved algorith m could determine proper clusters via fuzzy method while it can achieve robustness through possibilistic approach.…”

Section: B Introduction To Possibilistic Clustering Approachesmentioning

confidence: 99%

“…Second, a fu zzy membership that measured the relative degree of sharing of a point amongst all clusters. To integrate these two approaches, they interpret equation (6) as squared distance; they, then applied fuzzy clustering based on equation (6) to define their objective function shown in equation (13).…”

Section: B Introduction To Possibilistic Clustering Approachesmentioning

confidence: 99%

A Hierarchical Possibilistic Clustering

Haghighi¹,

Yazdi²,

Vahedian³

2009

IJCTE

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In this paper we propose to combine two clustering approaches, namely fuzzy and possibilistic c-means. While fuzzy c-means algorithm finds suitable clusters for groups of data points, obtained memberships of data, however, encounters a major deficiency caused by misinterpretation of membership values of data points. Therefore, membership values cannot correctly interpret compatibility or degree to which data points belong to clusters. As a result, noisy data will be misinterpreted by incorrect memberships assigned, as sum of memberships of each noisy data to all clusters is constrained to be equal to 1. To overcome this, a possibilistic approach has been proposed which removes this constraint. It has, however, caused another shortcoming as cluster centers converge to an identical point. Therefore, possibilities cannot correctly interpret the degrees of compatibilities. To correct this problem, a number of works have been carried out which all try to change possibilistic objective function proposed by Krishnapuram and James M. Keller.In this work, a hierarchical approach has been proposed based on properties of both fuzzy and possibilistic approaches to overcome this deficiency. Sensitivities of both methods have been studied together with analyzing results obtained by both methods. Superiority of the proposed method as opposed to conventional possibilistic c-means is shown to be conspicuous.

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2008

Clustering

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Improved Possibilistic C-Means Clustering Algorithms

Cited by 153 publications

References 12 publications

Studying possibility in a clustering algorithm for RBFNN design for function approximation

Studying possibility in a clustering algorithm for RBFNN design for function approximation

A Hierarchical Possibilistic Clustering

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