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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Bibliographic Details
Published in:Journal of classification Vol. 35; no. 2; pp. 345 - 366
Main Author: Roux, Maurice
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2018
Springer Nature B.V
Springer Verlag
Subjects:
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
Splitting procedures
Hierarchical clustering
Dissimilarity data
Dendrogram
Ultrametrics
Evaluation of hierarchy
ISSN:0176-4268, 1432-1343
Online Access:Get full text
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Summary: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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ISSN:0176-4268
1432-1343
DOI:10.1007/s00357-018-9259-9