Detection and Characterization of Cluster Substructure II. Fuzzy <i>c</i>-Varieties and Convex Combinations Thereof

Bezdek, James C.; Coray, Chris; Gunderson, Ragnhild; Watson, James

doi:10.1137/0140030

Cited by 177 publications

(67 citation statements)

References 9 publications

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“…Like FCM and GK, a number of these algorithms can also be generalized to deal with distributed data by means of the unified framework proposed in this chapter, such as: Gath and Geva (GG) [2,12], Fuzzy c-Varieties (FCV) [13], Fuzzy c-Elliptotypes (FCE) [14], Possibilistic c-Means (PCM) [3], Possibilistic Gustafson-Kessel (PGK) [3], Fuzzy-Possibilistic c-Means (FPCM) [15], and Possibilistic-Fuzzy c-Means (PFCM) [16]. Their computational time and space complexities are compared in Sect.…”

Section: Other Fuzzy Clustering Algorithmsmentioning

confidence: 99%

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Fuzzy Clustering Algorithms and Validity Indices for Distributed Data

Vendramin

Naldi

Campello

2014

Partitional Clustering Algorithms

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This chapter presents a unified framework to generalize a number of fuzzy clustering algorithms to handle distributed data in an exact way, i.e., with no approximation of results with respect to their original centralized versions. The same framework allows the exact distribution of relative validity indices used to evaluate the quality of fuzzy clustering solutions. Complexity analyses for each distributed algorithm and index are reported in terms of space, time, and communication aspects. A general procedure to estimate the number of clusters in a non-centralized fashion using the proposed framework is also described. Such a procedure is directly applicable not only to distributed data, but to parallel data processing scenarios as well. Experimental results illustrate the speedup obtained when running algorithms under the proposed framework in multiple cores of a processor, when compared to their traditional, centralized counterparts running in a single core. Additionally, the quality of the results and amount of data transmitted are assessed and compared among different fuzzy clustering algorithms.

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Section: Other Fuzzy Clustering Algorithmsmentioning

confidence: 99%

“…The FCE algorithm finds clusters in lines, planes, or hyper-planes, which have infinite length and may cluster widely separated collinear clusters together [2,6,14]. To avoid this problem, FCE [14] uses a distance given by a convex combination of (5.8) and (5.60) …”

Section: Fce: Fuzzy C-elliptotypesmentioning

confidence: 99%

Fuzzy Clustering Algorithms and Validity Indices for Distributed Data

Vendramin

Naldi

Campello

2014

Partitional Clustering Algorithms

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“…uma retaé infinita em sua extensão) e podem "unir" grupos que estão naturalmente separados (Bezdek et al, 1981b;Hoppner et al, 1999;Babuska, 1998). Para evitar esse problema, o algoritmo FCE (Fuzzy c-Elliptotypes -em inglês) (Bezdek et al, 1981b) utiliza uma distância modificada, dada por uma combinação convexa de (2.9) e (2.16) (1 ≤ i ≤ k, 1 ≤ j ≤ N ):…”

Section: Fce: Fuzzy C-elliptotypesunclassified

Estudo e desenvolvimento de algoritmos para agrupamento fuzzy de dados em cenários centralizados e distribuídos

Vendramin¹

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“…Fuzzy c-Varieties (FCV) [13] is a linear fuzzy clustering technique that captures the local linear structures by using linear varieties as the prototypes of clusters. In the FCV algorithm, the clustering criterion d ci is replaced with the distance between i-th data point and c-th linear variety as follows:…”

Section: Linear Fuzzy Clustering With Entropy Regularizationmentioning

confidence: 99%

“…Fuzzy c-Means (FCM) [8] and its derivatives [9,10,11] are closely related to GMMs and Ichihashi et al [12] proposed a clustering algorithm, which is similar to the EM algorithm for GMMs, by using the fuzzification technique with K-L information. Fuzzy c-Varieties (FCV) [13] is a linear fuzzy clustering technique that captures the local linear structures of data sets and is regarded as a Local PCA technique because the prototypes of clusters are estimated by solving the eigenvalue problems of fuzzy scatter matrices.…”

Section: Introductionmentioning

confidence: 99%

A unified view of probabilistic PCA and regularized linear fuzzy clustering

Mori

Honda

Kanda

et al.

Proceedings of the International Joint Conference on Neural Networks, 2003.

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FCM-type fuzzy clustering approaches are closely related to Gaussian Mixture Models (GMMs) and the objective function of Fuzzy c-Means with regularization by K-L information (KFCM) is optimized by an EM-like algorithm. In this paper, we propose to apply probabilistic PCA mixture models to linear clustering following the discussion on the relationship between Local PCA and linear fuzzy clustering. Although the proposed method is a kind of the constrained model of KFCM, the algorithm includes the Fuzzy c-Varieties (FCV) algorithm as a special case, and the algorithm can be regarded as a modified FCV algorithm with regularization by K-L information.

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Detection and Characterization of Cluster Substructure II. Fuzzy c-Varieties and Convex Combinations Thereof

Cited by 177 publications

References 9 publications

Fuzzy Clustering Algorithms and Validity Indices for Distributed Data

Fuzzy Clustering Algorithms and Validity Indices for Distributed Data

Estudo e desenvolvimento de algoritmos para agrupamento fuzzy de dados em cenários centralizados e distribuídos

A unified view of probabilistic PCA and regularized linear fuzzy clustering

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