Cluster merging and splitting in hierarchical clustering algorithms

Hierarchical clustering constructs a hierarchy of clusters by either repeatedly merging two smaller clusters into a larger one or splitting a larger cluster into smaller ones. The crucial step is how to best select the next cluster(s) to split or merge. Here we provide a comprehensive analysis of selection methods and propose several new methods. We perform extensive clustering experiments to test 8 selection methods, and find that the average similarity is the best method in divisive clustering and the MinMax linkage is the best in agglomerative clustering. Cluster balance is a key factor to achieve good performance. We also introduce the concept of objective function saturation and clustering target distance to effectively assess the quality of clustering.