A statistical model of cluster stability

Volkovich, Zeev; Barzily, Zeev; Morozensky, L.

doi:10.1016/j.patcog.2008.01.008

Cited by 40 publications

(16 citation statements)

References 35 publications

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“…This method has actually been offered in the papers Volkovich et al (2008Volkovich et al ( , 2009a in order to construct repeated clustering with a relation to geometrical cluster validation. Here, only one clusterer k is used.…”

Section: Second Simulation Methodsmentioning

confidence: 99%

“…It is natural to expect that distribution of these values constructed based sufficient amount of drawn samples pairs would be most concentrated at the origin in the case of the "true" number of clusters. This property can be established by many characteristics like empirical normalized mean or percentiles (see, for example, Lange et al 2003;Volkovich et al 2008). Here we offer to use another method, which deals with the distance's non-overlapping intervals of the same size.…”

Section: Algorithm Implementationmentioning

confidence: 99%

“…In the papers Volkovich et al (2008), Barzily et al (2009) and Volkovich and Barzily (2007) methods using the goodness of fit tests are suggested. The etalon cluster distributions are constructed here, using a model designed to represent well-mixed samples within the clusters.…”

Section: Introductionmentioning

confidence: 99%

“…Volkovich et al (2009a) use the binomial model of the K-Nearest Neighbors belonging to the own point's sample. Another model suggested by Volkovich et al (2008) and Barzily et al (2009), focuses on the distances between clustered samples drawn from the clusters cores and the whole population correspondingly.…”

Section: Introductionmentioning

confidence: 99%

“…As usual, the similarity is characterized via closeness offer of clusters contents, as measured, in fact, by the indicator probability metric. On the other hand, the papers of Volkovich et al (2008), Barzily et al (2009), Volkovich andBarzily (2007) and Volkovich et al (2009a) use variants of the goodness of fit tests based on the, so called, "well mingled samples" concept where in the case of the "true" number of clusters samples occurrences in clusters are suggested to be mingled to the extent they are mingled in whole population. Obviously, the contents based approaches can also be treated from this standpoint and closeness of samples occurrences can be evaluated by simple probability metrics (two-sample statistics test).…”

Section: Introductionmentioning

confidence: 99%

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Resampling approach for cluster model selection

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In cluster analysis, selecting the number of clusters is an "ill-posed" problem of crucial importance. In this paper we propose a re-sampling method for assessing cluster stability. Our model suggests that samples' occurrences in clusters can be considered as realizations of the same random variable in the case of the "true" number of clusters. Thus, similarity between different cluster solutions is measured by means of compound and simple probability metrics. Compound criteria result in validation rules employing the stability content of clusters. Simple probability metrics, in particular those based on kernels, provide more flexible geometrical criteria. We analyze several applications of probability metrics Editors: Süreyya Özögür-Akyüz, Devrim Ünay, and Alex Smola. Learn (2011) 85:209-248 combined with methods intended to simulate cluster occurrences. Numerical experiments are provided to demonstrate and compare the different metrics and simulation approaches.

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Section: Second Simulation Methodsmentioning

confidence: 99%

Section: Algorithm Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Resampling approach for cluster model selection

et al. 2011

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Use of the spectral clustering to determine coherent precipitation regions in Turkey for the period 1929–2007

Türkeş

Tatlı

2010

Intl Journal of Climatology

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ABSTRACT:In this study, we suggest the spectral clustering (SC), a hybrid clustering technique based on singular value decomposition (SVD) and K-means for grouping features of precipitation totals of 96 stations in Turkey. Clustering process establishes an exhaustive set of occupied regimes into distinct climatic zones. Results of the SC satisfactorily represent the influences of the synoptic-scale weather systems including such as the mid-latitude and Mediterranean frontal cyclones, and the mid-latitude travelling and eastern Europe high pressures in winter, sub-tropical Azores high pressure and monsoon low in summer. Results of the SC also well display the influences of local-scale atmospheric disturbances, and direct influences of physical geographical features of Turkey (i.e. exposure, topography, orography, land-sea distribution, continentality and the high Anatolian peninsula) on the geographical variability and coherent distribution of the annual precipitation totals over Turkey. Finally, based on the results of the SC method employed to annual precipitation totals of 96 stations in Turkey for the period of 1929-

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A Review of Cluster Validation with an Example of Type-2 Fuzzy Application in R

Özkan

Türkşen

2013

Advances in Type-2 Fuzzy Sets and Systems

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A statistical model of cluster stability

Cited by 40 publications

References 35 publications

Resampling approach for cluster model selection

Resampling approach for cluster model selection

Use of the spectral clustering to determine coherent precipitation regions in Turkey for the period 1929–2007

A Review of Cluster Validation with an Example of Type-2 Fuzzy Application in R

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