Hierarchical Means Clustering

Abstract

In the cluster analysis literature, there are several partitioning (non-hierarchical) methods for clustering multivariate objects based on model estimation. Distinct to these methods is the use of a system of n nested statistical models and the optimization of a loss function to best-fit a clustering model to observed data. Many hierarchical clustering methods are not model-based where hierarchy is obtained using a divisive or agglomerative greedy procedure. This paper aims to fill this gap by proposing a novel hierarchical cluster analysis methodology called Hierarchical Means Clustering. HMC produces a set of nested partitions with a centroid-based model estimated via least-squares by minimizing the total within-cluster deviance of the n partitions in the hierarchy. Hierarchical Means Clustering produces a hierarchy formed by n-1 nested partitions from 2 to n clusters with minimal total cluster deviance. Six real data examples are featured, and key links to k-means, Ward’s method, Bisecting k-means and model-based hierarchical agglomerative clustering methods are discussed.