Benchmarking Minimax Linkage

Abstract

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.