A modification to improve possibilistic fuzzy cluster analysis

Timm, Heiko; Kruse, Rudolf

doi:10.1109/fuzz.2002.1006721

Cited by 42 publications

(29 citation statements)

References 7 publications

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“…Using equation (8) for updating cluster centers, if we run the algorith m many times, for each cluster center βi we co mpute expectation or ensemble average of βi by equation (16) to indicate where the cluster center converges to.…”

Section: B Analytical Description Of Pcm Problemmentioning

confidence: 99%

“…The objective function proposed by Krishnapuram and Keller [3] is shown in equation (6). By min imizing the objective function, update formulas for ui,j , β i (center fo r cluster i) are indicated in equations (7,8,9). …”

Section: B Introduction To Possibilistic Clustering Approachesmentioning

confidence: 99%

“…In 2002, Timm and Kruse [8] solved the deficiency of PCM by adding a term to objective function of PCM proportion to inverse distance functions between cluster centers. In 2004, Jiang-She Zhang and Yiu-W ing Leung [13] changed the possibilistic approach given in [3] to overcome its drawbacks.…”

Section: B Introduction To Possibilistic Clustering Approachesmentioning

confidence: 99%

“…The constants a and b define the relative importance of fuzzy membership and typicality values in the objective function. Note that in (8), ui,j has the same mean ing of membership as that in FCM. Similarly, ti,j has the same interpretation of typicality as in PCM .…”

Section: B Introduction To Possibilistic Clustering Approachesmentioning

confidence: 99%

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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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Section: B Analytical Description Of Pcm Problemmentioning

confidence: 99%

Section: B Introduction To Possibilistic Clustering Approachesmentioning

confidence: 99%

Section: B Introduction To Possibilistic Clustering Approachesmentioning

confidence: 99%

Section: B Introduction To Possibilistic Clustering Approachesmentioning

confidence: 99%

See 2 more Smart Citations

A Hierarchical Possibilistic Clustering

Haghighi¹,

Yazdi²,

Vahedian³

2009

IJCTE

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“…The authors in [19] implement a modification of the PCM that solves the problem that PCM presents when it minimizes the distortion function placing the centers in the same position. To avoid the problem, a mutual repulsion of the clusters is proposed to be able to separate the cluster centers.…”

Section: Modified Possiblistic C-means (Mpcm)mentioning

confidence: 99%

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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