Cluster validity index for fuzzy clustering

Kwon, Soonhak

doi:10.1049/el:19981523

Cited by 249 publications

(113 citation statements)

References 3 publications

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“…Three well-known 2-D synthetic data sets, Butterfly, Example_01 and Example_02 presented in [19] and the other three 2-D synthetic data sets, Data_2_3_60, Data_2_3_70, and Data_2_4_110 [24], are shown in Figure 1 (a) to (f), respectively. Figure 2 shows the three 3-D synthetic data sets, Data_3_3_200, Data_3_3_300, and Data_3_4_320, respectively.…”

Section: Data Setsmentioning

confidence: 99%

Comparison and Weighted Summation Type of Fuzzy Cluster Validity Indices

Zhou

Ding

et al. 2014

INT J COMPUT COMMUN

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Finding the optimal cluster number and validating the partition results of a data set are difficult tasks since clustering is an unsupervised learning process. Cluster validity index (CVI) is a kind of criterion function for evaluating the clustering results and determining the optimal number of clusters. In this paper, we present an extensive comparison of ten well-known CVIs for fuzzy clustering. Then we extend traditional single CVIs by introducing the weighted method and propose a weighted summation type of CVI (WSCVI). Experiments on nine synthetic data sets and four real-world UCI data sets demonstrate that no one CVI performs better on all data sets than others. Nevertheless, the proposed WSCVI is more effective by properly setting the weights.

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Section: Data Setsmentioning

confidence: 99%

Comparison and Weighted Summation Type of Fuzzy Cluster Validity Indices

Zhou

Ding

et al. 2014

INT J COMPUT COMMUN

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“…The Kwon (K) index [63] is a modification of XB designed to eliminate its tendency to monotonically decrease when k approaches N and is given by…”

Section: K: Kwonmentioning

confidence: 99%

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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“…This index should be low when clusters are compact, so the optimal number of clusters can be found by minimization of (10). In order to decrease the tendency of XB (8) to monotonically decrease when c tends to n, Kwon add a penalty function [13], yielding to an index to be minimized:…”

Section: B Cluster Validity Procedures and Classical Fuzzy Indexesmentioning

confidence: 99%