Draft:Minimax linkage

In computational mathematics/statistics, minimax linkage is a criterion applied in hierarchical cluster analysis. Minimax linkage hierarchical clustering is a special case of the hierarchical clustering approaches, originally first introduced by Ao et al. in the AI genomics software project CLUSTAG in 2004. Medical institutions have been deploying the minimax linkage hierarchical clustering in their genomics research. Jacob Bien and Robert Tibshirani (2011) investigated the theoretical properties of the minimax linkage hierarchical clustering. Xiao Hui Tai and Kayla Frisoli (2021) conducted benchmarking for the minimax linkage hierarchical clustering. The development history of the minimax linkage criterion is shown as follows.

Minimax linkage in genomics applications
The complete linkage hierarchical clustering, minimax linkage hierarchical clustering and set cover algorithms were implemented in the program CLUSTAG for tag SNP selection.

Benchmarking the minimax linkage hierarchical clustering
Bien and Tibshirani (2011) used two real datasets to demonstrate the appeal of using minimax linkage compared with other linkages.

Tai and Frisoli (2021) reported that, similarly to Bien and Tibshirani (2011), minimax linkage often produced the smallest distances to prototypes, meaning that objects in a cluster were tightly clustered around their prototype.