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Minimax linkage is popular in bioinformatics, because it provides prototypes for each cluster.
The objective is the "minimum maximum distance", i.e., choose the merge
S. I. Ao, K. Yip, M. Ng, D. Cheung, P.-Y. Fong, I. Melhado, P. C. Sham
CLUSTAG: hierarchical clustering and graph methods for selecting tag SNPs
Bioinformatics, 21 (8)
J. Bien and R. Tibshirani
Hierarchical Clustering with Prototypes via Minimax Linkage
Journal of the American Statistical Association 106(495)
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