  Minimax linkage was first introduced by Ao et al. [3] in 2004, as an
alternative to standard linkage methods used in hierarchical clustering.
Minimax linkage relies on distances to a prototype for each cluster; this
prototype can be thought of as a representative object in the cluster, hence
improving the interpretability of clustering results. Bien and Tibshirani
analyzed properties of this method in 2011 [2], popularizing the method within
the statistics community. Additionally, they performed comparisons of minimax
linkage to standard linkage methods, making use of five data sets and two
different evaluation metrics (distance to prototype and misclassification
rate). In an effort to expand upon their work and evaluate minimax linkage more
comprehensively, our benchmark study focuses on thorough method evaluation via
multiple performance metrics on several well-described data sets. We also make
all code and data publicly available through an R package, for full
reproducibility. Similarly to [2], we find that minimax linkage often produces
the smallest maximum minimax radius of all linkage methods, meaning that
minimax linkage produces clusters where objects in a cluster are tightly
clustered around their prototype. This is true across a range of values for the
total number of clusters (k). However, this is not always the case, and special
attention should be paid to the case when k is the true known value. For true
k, minimax linkage does not always perform the best in terms of all the
evaluation metrics studied, including maximum minimax radius. This paper was
motivated by the IFCS Cluster Benchmarking Task Force's call for clustering
benchmark studies and the white paper [5], which put forth guidelines and
principles for comprehensive benchmarking in clustering. Our work is designed
to be a neutral benchmark study of minimax linkage.
