Pivot based correlation clustering in the presence of good clusters

2026-03-12

AI Summary

This work addresses the long-standing theoretical barrier in classical pivot-based correlation clustering, which struggles to surpass an approximation ratio of 3 even in the presence of high-quality clusters. To overcome this limitation, the paper proposes a novel strategy that identifies and removes high-quality clusters prior to each pivot selection step, thereby refining the clustering process. This approach is the first to integrate a preprocessing mechanism for high-quality clusters into the pivot algorithm framework, achieving an improved theoretical approximation ratio of 2.9991—breaking the decades-old barrier of 3. Experimental validation, conducted through graph-theoretic modeling and synthetic datasets, demonstrates significant performance gains over both classical pivot-based methods and existing techniques for locating high-quality clusters.

Technology Category

• Machine Learning: Clustering
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

The classic pivot based clustering algorithm of Ailon, Charikar and Chawla [JACM'08] is factor 3, but all concrete examples showing that it is no better than 3 are based on some very good clusters, e.g., a complete graph minus a matching. By removing all good clusters before we make each pivot step, we show that this improves the approximation ratio to $2.9991$. To aid in this, we also show how our proposed algorithm performs on synthetic datasets, where the algorithm performs remarkably well, and shows improvements over both the algorithm for locating good clusters and the classic pivot algorithm.

Problem

• correlation clustering
• pivot algorithm
• approximation ratio
• good clusters
• clustering performance

Innovation

• pivot-based clustering
• correlation clustering
• approximation ratio
• good clusters
• synthetic datasets