A new cluster-validity for fuzzy clustering

Zerhouni, Noureddine; Limouri, M.; Essaid, A.

doi:10.1016/s0031-3203(98)00157-5

Cited by 115 publications

(58 citation statements)

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“…Smaller V XIE means a more compact and well-separated c-partition. Zahid et al (1999) proposed the validity index V ZLE , based on a combination of two functions, each of which is given by a fuzzy separation-compactness ratio. The first function calculates this ratio by considering the geometrical properties and membership degrees of the data.…”

Section: Validity Indices For Fuzzy Clusteringmentioning

confidence: 99%

An objective approach to cluster validation

Bouguessa

Wang

2006

Pattern Recognition Letters

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Cluster validation is a major issue in cluster analysis. Many existing validity indices do not perform well when clusters overlap or there is significant variation in their covariance structure. The contribution of this paper is twofold. First, we propose a new validity index for fuzzy clustering. Second, we present a new approach for the objective evaluation of validity indices and clustering algorithms. Our validity index makes use of the covariance structure of clusters, while the evaluation approach utilizes a new concept of overlap rate that gives a formal measure of the difficulty of distinguishing between overlapping clusters. We have carried out experimental studies using data sets containing clusters of different shapes and densities and various overlap rates, in order to show how validity indices behave when clusters become less and less separable. Finally, the effectiveness of the new validity index is also demonstrated on a number of real-life data sets.

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Section: Validity Indices For Fuzzy Clusteringmentioning

confidence: 99%

An objective approach to cluster validation

Bouguessa

Wang

2006

Pattern Recognition Letters

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“…Several decades of research in the fields of pattern recognition and numerical taxonomy have produced a variety of heuristic indices of cluster validity that can guide selection of optimal fuzzy c-partitions (Bezdek 1981, Bezdek and Pal 1992, Pal and Bezdek 1995, Zahid et al 1999, Halkidi et al 2001. Some of these criteria utilize only the final fuzzy c-partition U while other validity functions incorporate the geometric structure of the original data to identify partitions that consist of compact (internally cohesive), separate (mutually distinctive) clusters (Gath andGeva 1989, Zahid et al 1999).…”

Section: Indices Of Cluster Validitymentioning

confidence: 99%

“…For detailed descriptions and derivations of these cluster validity criteria the interested reader is referred to the original publications; Zahid et al (1999), Pal and Bezdek (1995), and Halkidi et al (2001) provide useful summaries.…”

Section: Indices Of Cluster Validitymentioning

confidence: 99%

“…(Zahid et al 1999) Combines the FCM functional J m with a second term describing the separation between cluster centers and the overall mean of the data set. Smaller values of FS indicate a partition with compact, separate clusters, and the optimal c-partition minimizes FS.…”

Section: Xie-beni (1991) Cluster Validity Function Xbmentioning

confidence: 99%

“…Separateness-compactness index SC (Zahid et al 1999) This criterion incorporates both the partition U and the data X using fuzzy union and intersection operations. Higher values of c indicate good cohesion within clusters and a small overlap between pairs of clusters; maximizing SC provides a well-defined fuzzy c-partition.…”

Section: Fuzzy Hypervolume Fhv (Gath and Geva 1989)mentioning

confidence: 99%

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Alternative representations of in‐stream habitat: classification using remote sensing, hydraulic modeling, and fuzzy logic

Legleiter

Goodchild

2005

International Journal of Geographical Information Science

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Improved techniques are needed to characterize complex fluvial systems and monitor ecologically important, yet highly vulnerable riverine environments. This paper explores potential alternatives to traditional mapping of in-stream habitat and presents fuzzy set theory as a means of departing from the rigid, Boolean, object-based framework. We utilize hydrodynamic modeling, remotely sensed data, and fuzzy clustering to obtain classifications that allow for continuous partial membership and gradual transitions among habitat types. Methods of assessing cluster validity are available, but data quality is a crucial consideration. Crisp, vector-based representations can be derived from raster fuzzy classifications by applying a threshold to maximum membership values. This process results in conditional objects separated by ambiguous transition zones, and a compromise must be reached between the proportion of the channel assigned to polygons and the certainty with which this assignment can be made. Spatial patterns of classification uncertainty can also be used to identify areas of confusion, infer boundaries of variable width, and highlight areas of increased habitat diversity. Hydraulic modeling and remote sensing complement one another and, together with field work, could provide a more realistic representation of the fluvial environment.

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Opportunistic channel allocation decision making in cognitive radio communications

Shatila

Khedr

Reed

2012

Int J Communication

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SUMMARYThe global spread of wireless devices with mobile Internet access and the increasing demand of multimedia‐based applications are fueling the need for wireless broadband networks. IEEE 802.16 and 802.20 are standards for a broadband wireless access with promising cognitive radio features to support mobile Internet access. However, because of the fast changing radio environment and the demand for dynamic spectrum allocation mechanisms, these standards must continuously readjust different radio parameters. The cognitive radio makes decisions based on its built‐in inference engine, which also in time can adapt itself to different situations through the process of learning from experience. In this paper we present an automated opportunistic decision making and learning process for cognitive radio based on uncertainty reasoning algorithms. This novel approach is well suited in fast changing wireless environments with vague, incomplete, and heterogeneous information. Theory and simulations prove that decision making and learning of the cognitive radio based on the proposed approach cope with the changes in the radio environment. In this work we use fuzzy logic for the learning and decision making of the cognitive radio. Simulation also show that our approach provides accurate and precise decisions on allocating spectrum to mobile Internet users even in fast varying radio conditions. Copyright © 2012 John Wiley & Sons, Ltd.

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A new cluster-validity for fuzzy clustering

Cited by 115 publications

References 0 publications

An objective approach to cluster validation

An objective approach to cluster validation

Alternative representations of in‐stream habitat: classification using remote sensing, hydraulic modeling, and fuzzy logic

Opportunistic channel allocation decision making in cognitive radio communications

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