Efficient Centroid-Linkage Clustering

Mohammadhossein Bateni, Laxman Dhulipala, Willem Fletcher, Kishen N Gowda, D Ellis Hershkowitz, Rajesh Jayaram, Jakub Lacki

Keywords: clustering, hierarchical agglomerative clustering, hac, centroid linkage, algorithm, dynamic nearest neighbor search, adaptive updates

TL;DR: We give an efficient algorithm for Centroid-Linkage Hierarchical Agglomerative Clustering (HAC), which computes a $c$-approximate clustering in $n^{1+1/c^2+o(1)}$ time and obtains significant speedups over existing baselines.

Abstract:

We give an 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.

Primary Area: Infrastructure (libraries, improved implementation and scalability, distributed solutions)

Submission Number: 11429