Efficient Centroid-Linkage Clustering

TL;DR

This paper introduces an efficient approximation algorithm for Centroid-Linkage Hierarchical Clustering that significantly speeds up computation while maintaining clustering quality, supported by empirical evaluation.

Contribution

It presents a novel $c$-approximate clustering algorithm with a new dynamic data structure for nearest neighbor search, improving speed over existing methods.

Findings

Achieves up to 36x speedup over exact baseline

Maintains clustering quality comparable to state-of-the-art methods

Provides empirical evidence of efficiency and accuracy

Abstract

We give an efficient algorithm for Centroid-Linkage Hierarchical Agglomerative Clustering (HAC), which computes a $c$-approximate clustering in roughly $n^{1+O(1/c^2)}$ time. We obtain our result by combining a new Centroid-Linkage HAC algorithm with a novel fully dynamic data structure for nearest neighbor search which works under adaptive updates. We also evaluate our algorithm empirically. By leveraging a state-of-the-art nearest-neighbor search library, we obtain a fast and accurate Centroid-Linkage HAC algorithm. Compared to an existing state-of-the-art exact baseline, our implementation maintains the clustering quality while delivering up to a $36\times$ speedup due to performing fewer distance comparisons.