Hierarchical Clustering: $O(1)$-Approximation for Well-Clustered Graphs

• URL: http://arxiv.org/abs/2112.09055v1
• Date: Thu, 16 Dec 2021 17:52:04 GMT
• Title: Hierarchical Clustering: $O(1)$-Approximation for Well-Clustered Graphs
• Authors: Bogdan-Adrian Manghiuc and He Sun
• Abstract summary: We present two-time approximation algorithms for hierarchical clustering. The significance of our work is demonstrated by the empirical analysis on both synthetic and real-world data sets.
• Score: 3.2901541059183432
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hierarchical clustering studies a recursive partition of a data set into clusters of successively smaller size, and is a fundamental problem in data analysis. In this work we study the cost function for hierarchical clustering introduced by Dasgupta, and present two polynomial-time approximation algorithms: Our first result is an $O(1)$-approximation algorithm for graphs of high conductance. Our simple construction bypasses complicated recursive routines of finding sparse cuts known in the literature. Our second and main result is an $O(1)$-approximation algorithm for a wide family of graphs that exhibit a well-defined structure of clusters. This result generalises the previous state-of-the-art, which holds only for graphs generated from stochastic models. The significance of our work is demonstrated by the empirical analysis on both synthetic and real-world data sets, on which our presented algorithm outperforms the previously proposed algorithm for graphs with a well-defined cluster structure.

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