Comparative evaluation of two superior stopping rules for hierarchical cluster analysis

Atlas, Robert S.; Overall, John E.

doi:10.1007/bf02294393

Cited by 42 publications

(45 citation statements)

References 14 publications

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“…To decrease the differences among the clusters, primary clusters were formed using Ward's minimum variance hierarchical cluster technique (Ward, 1963). This technique is often considered useful to improve the underlying data structure (Atlas & Overall, 1994;Blashfield, 1976).…”

Section: Determination Of Clustersmentioning

confidence: 99%

Effects of Secondary School Students’ Perceptions of Mathematics Education Quality on Mathematics Anxiety and Achievement

Çiftçi¹

2015

EDUC SCI-THEOR PRACT

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The two aims of this study are as follows: (i) to compare the differences in mathematics anxiety and achievement in secondary school students according to their perceptions of the quality of their mathematics education via a cluster analysis and (ii) to test the effects of the perception of mathematics education quality on anxiety and achievement via structural equation modeling. The research was designed using a causal design; the mathematics education quality comprised the independent variable, whereas mathematics anxiety and achievement comprised the dependent variables. This study was conducted with 638 secondary school students from schools located at the city center of Eskisehir, spread in the region [lower, middle and upper] according to the socio-economic classification of TUIK, which is referred to as layered sampling. Data were collected using the Mathematics Education Quality Scale and the Mathematics Anxiety Assessment Scale, whereas student achievement levels were obtained from the Placement Test [TEOG] score and the mathematics grade point average [GPA]. The data obtained in this study were analyzed using Ward's minimum variance hierarchical cluster, discriminant, ANOVA, MANOVA, paired-samples t-test and path analysis. The findings were grouped as (i) input, (ii) process and (iii) output clusters, which each presented different perceptions of secondary school students regarding the quality of mathematics education. In addition, these findings also indicated that mathematics education quality perception positively affects the TEOG and mathematics GPA, whereas it negatively affects mathematics anxiety.

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Section: Determination Of Clustersmentioning

confidence: 99%

Effects of Secondary School Students’ Perceptions of Mathematics Education Quality on Mathematics Anxiety and Achievement

Çiftçi¹

2015

EDUC SCI-THEOR PRACT

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“…However, due to the truncation step in the algorithm, the method is incapable of simulating clusters with wide ranges of separation [111] that can be misleading [5]. Many other proposed methods [19,49,63,84,100] share similar shortcomings.…”

Section: Simulating Mixture Distributions For Evaluating Clustering Amentioning

confidence: 99%

“…Many other proposed methods [19,49,63,84,100] share similar shortcomings. An attempt to control the level of overlap between any two components using intra-class correlations was made by [5] who however admitted that it still lacked the ability to provide a "perceptually meaningful description" of overlap (see page 583). The notion of c-separation was introduced by [34] in the context of learning Gaussian mixtures.…”

Section: Simulating Mixture Distributions For Evaluating Clustering Amentioning

confidence: 99%

Finite mixture models and model-based clustering

Melnykov¹,

Maitra²

2010

Statist. Surv.

266

162

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Finite mixture models have a long history in statistics, having been used to model population heterogeneity, generalize distributional assumptions, and lately, for providing a convenient yet formal framework for clustering and classification. This paper provides a detailed review into mixture models and model-based clustering. Recent trends as well as open problems in the area are also discussed. Abstract: Finite mixture models have a long history in statistics, having been used to model population heterogeneity, generalize distributional assumptions, and lately, for providing a convenient yet formal framework for clustering and classification. This paper provides a detailed review into mixture models and model-based clustering. Recent trends as well as open problems in the area are also discussed. Keywords

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“…Similar shortcomings are also characteristic of methods proposed by Blashfield (1976), Kuiper and Fisher (1975), Gold and Hoffman (1976), McIntyre and Blashfield (1980) and Price (1993). Atlas and Overall (1994) manipulated intra-class correlation to control cluster overlap, but they mention that their description is not "perceptually meaningful" (p. 583). Waller, Underhill and Kaiser (1999) provided a qualitative approach to controlling cluster overlap which lacks quantitation and can not be extended to high dimensions.…”

mentioning

confidence: 71%

“…Milligan (1985) developed a widely-used algorithm that generates well-separated clusters from truncated multivariate normal distributions. But the algorithm's statements on degree of separation may be unrealistic (Atlas and Overall 1994) and thus clustering methods can not be fully evaluated under wide ranges of conditions (Steinley and Henson 2005). Similar shortcomings are also characteristic of methods proposed by Blashfield (1976), Kuiper and Fisher (1975), Gold and Hoffman (1976), McIntyre and Blashfield (1980) and Price (1993).…”

mentioning

confidence: 99%

Simulating Data to Study Performance of Finite Mixture Modeling and Clustering Algorithms

Maitra

Melnykov

2010

Journal of Computational and Graphical Statistics

132

125

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A new method is proposed to generate sample Gaussian mixture distributions according to pre-specified overlap characteristics. Such methodology is useful in the context of evaluating performance of clustering algorithms. Our suggested approach involves derivation of and calculation of the exact overlap between every cluster pair, measured in terms of their total probability of misclassification, and then guided simulation of Gaussian components satisfying pre-specified overlap characteristics. The algorithm is illustrated in two and five dimensions using contour plots and parallel distribution plots, respectively, which we introduce and develop to display mixture distributions in higher dimensions. We also study properties of the algorithm and variability in the simulated mixtures. The utility of the suggested algorithm is demonstrated via a study of initialization strategies in Gaussian clustering.

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Comparative evaluation of two superior stopping rules for hierarchical cluster analysis

Abstract: cluster analysis, hierarchical, stopping rule, cluster distances, population overlap,

Cited by 42 publications

References 14 publications

Effects of Secondary School Students’ Perceptions of Mathematics Education Quality on Mathematics Anxiety and Achievement

Effects of Secondary School Students’ Perceptions of Mathematics Education Quality on Mathematics Anxiety and Achievement

Finite mixture models and model-based clustering

Simulating Data to Study Performance of Finite Mixture Modeling and Clustering Algorithms

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