Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method

Székely, Gábor; Rizzo, Maria L.

doi:10.1007/s00357-005-0012-9

Cited by 550 publications

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“…Székely and Rizzo have recently described "a joint between-within e-distance between clusters" that encompasses both intra-cluster homogeneity and inter-cluster heterogeneity, and use this distance as the criterion for a generalized clustering method that includes Ward's method as a limiting case [18]. Specifically, Székely and Rizzo define the between-within distance, or e-distance e(A,B), between two clusters A and B , containing n a and n b objects respectively, as , where the exponent α is in the range 0 < α ≤ 2 and where ║X-Y║ is the Euclidean distance between two objects X and Y. Székely and Rizzo focus on two special cases: α = 2 and α = 1.…”

Section: The Székely-rizzo Clustering Methodsmentioning

confidence: 99%

“…They note that the second of these cases, e 1 (A,B), has several desirable theoretical properties, one of which (that of statistical consistency as defined by Kaufman and Rousseeuw [22]) is not exhibited by e 2 (A,B) (i.e., Ward's method). They suggest that clusters based on e 1 (A,B) will be superior to those based on e 2 (A,B) for separating clusters with the same, or close, cluster means but different distributions of points around those means, and use dermatological, gene expression and simulated multivariate normal datasets to demonstrate that e 1 (A,B) can indeed out-perform e 2 (A,B) in some circumstances [18]. The Székely-Rizzo clustering method is available as a contributed package, called Energy, in the R statistical system (available from http://www.r-project.org/), and this was used for all the experiments reported below.…”

Section: The Székely-rizzo Clustering Methodsmentioning

confidence: 99%

“…Székely and Rizzo have recently described a new hierarchical agglomerative clustering method [18]. This method generalizes Ward's method by defining a cluster distance and objective function in terms of a power in the interval (0,2] of the Euclidean distance between cluster centres, with Ward's method being obtained as the limiting case when the power is 2.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Clustering files of chemical structures using the Székely–Rizzo generalization of Ward's method

Varin

Bureau

Mueller

et al. 2009

Journal of Molecular Graphics and Modelling

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Ward's method is extensively used for clustering chemical structures represented by 2D fingerprints. This paper compares Ward clusterings of 14 datasets (containing between 278 and 4332 molecules) with those obtained using the Székely-Rizzo clustering method, a generalization of Ward's method. The clusters resulting from these two methods were evaluated by the extent to which the various classifications were able to group active molecules together, using a novel criterion of clustering effectiveness. Analysis of a total of 1400 classifications (Ward and Székely-Rizzo clustering methods, fourteen different datasets, five different fingerprints and ten different distance coefficients) demonstrated the general superiority of the Székely-Rizzo method. The distance coefficient first described by Soergel performed extremely well in these experiments, and this was also the case when it was used in simulated virtual screening experiments.

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Section: The Székely-rizzo Clustering Methodsmentioning

confidence: 99%

Section: The Székely-rizzo Clustering Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Clustering files of chemical structures using the Székely–Rizzo generalization of Ward's method

Varin

Bureau

Mueller

et al. 2009

Journal of Molecular Graphics and Modelling

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“…Four of them-Ward, Complete, Average and Single-are well-known. Energy is a new method [34] and has never been evaluated in chemical clustering. Single, complete and average linkage define the intercluster distances as the minimum, maximum, and average values, respectively, between two clusters [35 -37].…”

Section: Clustering Algorithmsmentioning

confidence: 99%

“…Single, complete and average linkage define the intercluster distances as the minimum, maximum, and average values, respectively, between two clusters [35 -37]. Ward [38] and Energy [34] methods consider homogeneity and separability of the different clusters as a basis for the clustering. In contrast to the linkage method, these methods do not group together clusters with the smallest distances, but unify clusters such that the internal variation (dissimilarity values) does not increase too drastically.…”

Section: Clustering Algorithmsmentioning

confidence: 99%

3D Pharmacophore, hierarchical methods, and 5-HT₄ receptor binding data

Varin

Saettel

Villain

et al. 2008

Journal of Enzyme Inhibition and Medicinal Chemistry

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5-Hydroxytryptamine subtype-4 (5-HT 4 ) receptors have stimulated considerable interest amongst scientists and clinicians owing to their importance in neurophysiology and potential as therapeutic targets. A comparative analysis of hierarchical methods applied to data from one thousand 5-HT 4 receptor -ligand binding interactions was carried out. The chemical structures were described as chemical and pharmacophore fingerprints. The definitions of indices, related to the quality of the hierarchies in being able to distinguish between active and inactive compounds, revealed two interesting hierarchies with the Unity (1 active cluster) and pharmacophore fingerprints (4 active clusters). The results of this study also showed the importance of correct choice of metrics as well as the effectiveness of a new alternative of the Ward clustering algorithm named Energy (Minimum E-Distance method). In parallel, the relationship between these classifications and a previously defined 3D 5-HT 4 antagonist pharmacophore was established.

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Hierarchical clustering

Cichosz

2015

Data Mining Algorithms

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Clustering techniques have a wide use and importance nowadays. This importance tends to increase as the amount of data grows and the processing power of the computers increases. Clustering applications are used extensively in various fields such as artificial intelligence, pattern recognition, economics, ecology, psychiatry and marketing.There are several algorithms and methods have been developed for clustering problem. But problem are always arises for finding a new algorithm and process for extracting knowledge for improving accuracy and efficiency. This type of dilemma motivated us to develop new algorithm and process for clustering problems. There are several another issue are also exits like cluster analysis can contribute in compression of the information included in data. In several cases, the amount of available data is very large and its processing becomes very demanding. Clustering can be used to partition data set into a number of "interesting" clusters. Then, instead of processing the data set as an entity, we adopt the representatives of the defined clusters in our process. Thus, data compression is achieved. Cluster analysis is applied to the data set and the resulting clusters are characterized by the features of the patterns that belong to these clusters. Then, unknown patterns can be classified into specified clusters based on their similarity to the clusters' features. Useful knowledge related to our data can be extracted [1].

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Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method

Cited by 550 publications

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Clustering files of chemical structures using the Székely–Rizzo generalization of Ward's method

Clustering files of chemical structures using the Székely–Rizzo generalization of Ward's method

3D Pharmacophore, hierarchical methods, and 5-HT₄ receptor binding data

Hierarchical clustering

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Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method

Cited by 550 publications

References 0 publications

Clustering files of chemical structures using the Székely–Rizzo generalization of Ward's method

Clustering files of chemical structures using the Székely–Rizzo generalization of Ward's method

3D Pharmacophore, hierarchical methods, and 5-HT4 receptor binding data

Hierarchical clustering

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3D Pharmacophore, hierarchical methods, and 5-HT₄ receptor binding data