Agglomerative Hierarchical Clustering
Lynne Billard, Edwin Diday · 2019
This chapter focuses on agglomerative hierarchical clustering. Agglomerative hierarchical clustering occurs when starting from the base of the hierarchical tree with each branch/node consisting of one observation only and where observations are progressively clustered into larger clusters until the top of the hierarchy tree is reached with all observations in a single cluster. The chapter considers the process where at any level of the tree, clusters are non-overlapping to produce hierarchical trees. Agglomerative algorithms are applied to multi-valued list (modal and non-modal) observations, interval-valued observations, histogram-valued observations, and mixed-valued observations. The chapter also considers an example where the data appear at first hand to be interval-valued, but where, after the application of logical rules, the data become histogram-valued in reality. When clusters are allowed to overlap, people have pyramidal clustering. The chapter illustrates the distinction between these two trees.