Modern hierarchical, agglomerative clustering algorithms

TL;DR

This paper introduces efficient algorithms for hierarchical agglomerative clustering, including a new versatile algorithm, validates existing methods, and provides practical recommendations for various clustering schemes.

Contribution

It presents a new, more efficient algorithm suitable for any distance update scheme and validates existing algorithms, offering practical guidance for modern clustering tasks.

Findings

New algorithm outperforms existing methods in efficiency

Validated correctness of Rohlf and Murtagh's algorithms

Provided recommendations for best algorithms in different schemes

Abstract

This paper presents algorithms for hierarchical, agglomerative clustering which perform most efficiently in the general-purpose setup that is given in modern standard software. Requirements are: (1) the input data is given by pairwise dissimilarities between data points, but extensions to vector data are also discussed (2) the output is a "stepwise dendrogram", a data structure which is shared by all implementations in current standard software. We present algorithms (old and new) which perform clustering in this setting efficiently, both in an asymptotic worst-case analysis and from a practical point of view. The main contributions of this paper are: (1) We present a new algorithm which is suitable for any distance update scheme and performs significantly better than the existing algorithms. (2) We prove the correctness of two algorithms by Rohlf and Murtagh, which is necessary in each case for different reasons. (3) We give well-founded recommendations for the best current algorithms for the various agglomerative clustering schemes.