A mixed c-means clustering model

Pal, Nikhil R.; Pal, Krishan; Bezdek, James C.

doi:10.1109/fuzzy.1997.616338

Cited by 266 publications

(138 citation statements)

References 7 publications

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“…As mentioned earlier, evaluating objective function (6) reveals that, it is min imized only if all cluster centers are very close or even the same. The reason is that the equation (7) for updating membership degree of a data point to a cluster depends only on distance of the data point to the cluster, while it does not depend on the distance to other clusters.…”

Section: A Issues With Pcmmentioning

confidence: 94%

“…By evaluating results shown in Table 1, it is evident that cluster centers in all examp les are very close to each other, and almost identical. This undesired effect, which is due to minimizing the objective function shown in equation (6), causes misinterpretation of co mpatibilities of data points to clusters. In Table 1, average d istances between cluster centers for wine and Wpbc data sets seem to be more than in other data sets.…”

Section: B Analytical Description Of Pcm Problemmentioning

confidence: 99%

“…By analyzing many different samples and recalling equations (20-24), it is obvious that, if based on some criteria, initial values of U are selected correctly, the PCM algorith m works well. By randomly init ializing membership values, cluster centers converge to some identical point to minimize equation (6). This effect is shown in Table 1 by executing PCM algorith m on some known data sets.…”

Section: B Analytical Description Of Pcm Problemmentioning

confidence: 99%

“…The objective function (which satisfies the requirements) obtained by adding a penalty term to the objective function of FCM in equation (3). 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%

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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: A Issues With Pcmmentioning

confidence: 94%

Section: B Analytical Description Of Pcm Problemmentioning

confidence: 99%

Section: B Analytical Description Of Pcm Problemmentioning

confidence: 99%

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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“…The corresponding IFPCM-algorithm is developed by hybridizing concepts of the FPCM clustering method [22], intuitionistic fuzzy sets and distance measures. The IFPCM-algorithm resolves inherent problems encountered with information regarding membership values of objects to each cluster by generalizing membership and nonmembership with hesitancy degree.…”

Section: Related Workmentioning

confidence: 99%

Intuitionistic Heuristic Prototype-based Algorithm of Possibilistic Clustering

Viattchenin¹,

Shyrai²

2015

CAE

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This paper introduces a novel intuitionistic fuzzy set-based heuristic algorithm of possibilistic clustering. For the purpose, some remarks on the fuzzy approach to clustering are discussed and a brief review of intuitionistic fuzzy set-based clustering procedures is given, basic concepts of the intuitionistic fuzzy set theory and the intuitionistic fuzzy generalization of the heuristic approach to possibilistic clustering are considered, a general plan of the proposed clustering procedure is described in detail, two illustrative examples confirm good performance of the proposed algorithm, and some preliminary conclusions are formulated.

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