Chamfer-Linkage for Hierarchical Agglomerative Clustering

2026-02-11

AI Summary

This work proposes Chamfer-linkage, a novel linkage criterion for agglomerative hierarchical clustering that integrates the Chamfer distance as a measure of inter-cluster dissimilarity. Classical linkage functions—such as single, average, and Ward’s linkage—often yield inconsistent and suboptimal clustering performance on real-world data. In contrast, Chamfer-linkage offers both strong theoretical properties and computational efficiency, operating in O(n²) time complexity. Empirical evaluations across multiple real-world datasets demonstrate that the proposed method consistently outperforms established linkage strategies, establishing it as a high-performance, plug-and-play alternative for hierarchical clustering tasks.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Data Compression
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Hierarchical Agglomerative Clustering (HAC) is a widely-used clustering method based on repeatedly merging the closest pair of clusters, where inter-cluster distances are determined by a linkage function. Unlike many clustering methods, HAC does not optimize a single explicit global objective; clustering quality is therefore primarily evaluated empirically, and the choice of linkage function plays a crucial role in practice. However, popular classical linkages, such as single-linkage, average-linkage and Ward's method show high variability across real-world datasets and do not consistently produce high-quality clusterings in practice. In this paper, we propose \emph{Chamfer-linkage}, a novel linkage function that measures the distance between clusters using the Chamfer distance, a popular notion of distance between point-clouds in machine learning and computer vision. We argue that Chamfer-linkage satisfies desirable concept representation properties that other popular measures struggle to satisfy. Theoretically, we show that Chamfer-linkage HAC can be implemented in $O(n^2)$ time, matching the efficiency of classical linkage functions. Experimentally, we find that Chamfer-linkage consistently yields higher-quality clusterings than classical linkages such as average-linkage and Ward's method across a diverse collection of datasets. Our results establish Chamfer-linkage as a practical drop-in replacement for classical linkage functions, broadening the toolkit for hierarchical clustering in both theory and practice.

Problem

• Hierarchical Agglomerative Clustering
• linkage function
• clustering quality
• Chamfer distance

Innovation

• Chamfer-linkage
• Hierarchical Agglomerative Clustering
• Chamfer distance
• linkage function
• cluster quality