A cost function for similarity-based hierarchical clustering

TL;DR

This paper introduces a new cost function for similarity-based hierarchical clustering, enabling more precise and theoretically justified clustering algorithms with provable approximation guarantees.

Contribution

The paper proposes a novel cost function for hierarchical clustering based on pairwise similarities, along with a top-down construction method and approximation analysis.

Findings

The cost function behaves sensibly in canonical instances.

The proposed method admits a top-down construction with a provably good approximation ratio.

Provides a new objective for hierarchical clustering algorithms.

Abstract

The development of algorithms for hierarchical clustering has been hampered by a shortage of precise objective functions. To help address this situation, we introduce a simple cost function on hierarchies over a set of points, given pairwise similarities between those points. We show that this criterion behaves sensibly in canonical instances and that it admits a top-down construction procedure with a provably good approximation ratio.