Ward's Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm

TL;DR

This paper reviews Ward's hierarchical clustering method, clarifies its interpretations and implementations, and provides case studies to aid software development for data analysis.

Contribution

It offers a comprehensive survey and comparison of Ward's clustering criterion and algorithms, addressing inconsistencies in literature and software implementations.

Findings

Different interpretations of Ward's method exist in literature.

Various software implementations use differing agglomerative criteria.

The paper provides guidance for consistent software development.

Abstract

The Ward error sum of squares hierarchical clustering method has been very widely used since its first description by Ward in a 1963 publication. It has also been generalized in various ways. However there are different interpretations in the literature and there are different implementations of the Ward agglomerative algorithm in commonly used software systems, including differing expressions of the agglomerative criterion. Our survey work and case studies will be useful for all those involved in developing software for data analysis using Ward's hierarchical clustering method.