Nearly-Optimal Hierarchical Clustering for Well-Clustered Graphs

TL;DR

This paper introduces two nearly-linear time hierarchical clustering algorithms for well-structured graphs that achieve constant-factor approximation of Dasgupta's cost, outperforming previous methods on synthetic and real datasets.

Contribution

The paper proposes efficient HC algorithms with theoretical guarantees and demonstrates superior empirical performance on diverse datasets.

Findings

Algorithms run in nearly-linear time.

Achieve O(1) approximation of Dasgupta's cost.

Produce comparable or better HC trees faster than prior methods.

Abstract

This paper presents two efficient hierarchical clustering (HC) algorithms with respect to Dasgupta's cost function. For any input graph $G$ with a clear cluster-structure, our designed algorithms run in nearly-linear time in the input size of $G$, and return an $O(1)$-approximate HC tree with respect to Dasgupta's cost function. We compare the performance of our algorithm against the previous state-of-the-art on synthetic and real-world datasets and show that our designed algorithm produces comparable or better HC trees with much lower running time.