Expanding the class of global objective functions for dissimilarity-based hierarchical clustering

TL;DR

This paper introduces a broad new class of global objective functions for dissimilarity-based hierarchical clustering, unifying and extending existing methods with theoretical guarantees and phylogenetic-inspired algorithms.

Contribution

It proposes a new class of objective functions that encompass many existing clustering methods and provides insights into their greedy algorithms based on these objectives.

Findings

Many clustering methods are greedy algorithms for the new objectives.

The new objectives satisfy desirable properties from prior work.

The approach is inspired by concepts in phylogenetics.

Abstract

Recent work on dissimilarity-based hierarchical clustering has led to the introduction of global objective functions for this classical problem. Several standard approaches, such as average linkage, as well as some new heuristics have been shown to provide approximation guarantees. Here we introduce a broad new class of objective functions which satisfy desirable properties studied in prior work. Many common agglomerative and divisive clustering methods are shown to be greedy algorithms for these objectives, which are inspired by related concepts in phylogenetics.