A Comparative Study of Divisive and Agglomerative Hierarchical Clustering Algorithms
A general scheme for divisive hierarchical clustering algorithms is proposed. It is made of three main steps: first a splitting procedure for the subdivision of clusters into two subclusters, second a local evaluation of the bipartitions resulting from the tentative splits and, third, a formula for...
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| Veröffentlicht in: | Journal of classification Jg. 35; H. 2; S. 345 - 366 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer US
01.07.2018
Springer Nature B.V Springer Verlag |
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| ISSN: | 0176-4268, 1432-1343 |
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| Abstract | A general scheme for divisive hierarchical clustering algorithms is proposed. It is made of three main steps: first a splitting procedure for the subdivision of clusters into two subclusters, second a local evaluation of the bipartitions resulting from the tentative splits and, third, a formula for determining the node levels of the resulting dendrogram. A set of 12 such algorithms is presented and compared to their agglomerative counterpart (when available). These algorithms are evaluated using the Goodman-Kruskal correlation coefficient. As a global criterion it is an internal goodness-of-fit measure based on the set order induced by the hierarchy compared to the order associated with the given dissimilarities. Applied to a hundred random data tables and to three real life examples, these comparisons are in favor of methods which are based on unusual ratio-type formulas to evaluate the intermediate bipartitions, namely the Silhouette formula, the Dunn's formula and the Mollineda et al. formula. These formulas take into account both the within cluster and the between cluster mean dissimilarities. Their use in divisive algorithms performs very well and slightly better than in their agglomerative counterpart. |
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| AbstractList | A general scheme for divisive hierarchical clustering algorithms is proposed. It is made of three main steps: first a splitting procedure for the subdivision of clusters into two subclusters, second a local evaluation of the bipartitions resulting from the tentative splits and, third, a formula for determining the node levels of the resulting dendrogram. A set of 12 such algorithms is presented and compared to their agglomerative counterpart (when available). These algorithms are evaluated using the Goodman-Kruskal correlation coefficient. As a global criterion it is an internal goodness-of-fit measure based on the set order induced by the hierarchy compared to the order associated with the given dissimilarities. Applied to a hundred random data tables and to three real life examples, these comparisons are in favor of methods which are based on unusual ratio-type formulas to evaluate the intermediate bipartitions, namely the Silhouette formula, the Dunn's formula and the Mollineda et al. formula. These formulas take into account both the within cluster and the between cluster mean dissimilarities. Their use in divisive algorithms performs very well and slightly better than in their agglomerative counterpart. |
| Author | Roux, Maurice |
| Author_xml | – sequence: 1 givenname: Maurice surname: Roux fullname: Roux, Maurice email: mrhroux@yahoo.fr organization: IMBE (Aix Marseille Université, CNRS, IRD, Univ Avignon), Faculté des Sciences de St-Jérôme |
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| Keywords | Splitting procedures Hierarchical clustering Dissimilarity data Dendrogram Ultrametrics Evaluation of hierarchy |
| Language | English |
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| SubjectTerms | Agglomeration Algorithms Bioinformatics Cluster analysis Clustering Comparative analysis Comparative studies Correlation coefficients Goodness of fit Hierarchies Marketing Mathematics and Statistics Morality Other Statistics Pattern Recognition Psychometrics Signal,Image and Speech Processing Statistical Theory and Methods Statistics |
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| Title | A Comparative Study of Divisive and Agglomerative Hierarchical Clustering Algorithms |
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