Correlation Clustering with Random Partial Information

2026-08-17

AI Summary

This study addresses the challenge of significantly degraded approximation ratios for correlation clustering on incomplete graphs compared to complete graphs. Focusing on random edge deletion models, we propose a novel approximation algorithm based on random subsampling. Theoretically, we prove that this approach surpasses general graph lower bounds within the class of random partial information graphs, yielding superior approximation guarantees over traditional methods. Experimental results further demonstrate that the algorithm’s performance approaches that achievable on complete graphs. By effectively bridging the theoretical gap between complete and general graphs, this work provides a solution for correlation clustering under incomplete data that combines rigorous theoretical foundations with practical utility.

Abstract

Correlation clustering is a fundamental unsupervised learning problem. On complete graphs, both the min-disagreement and min-max objectives admit constant-factor approximations, yet on general (non-complete) graphs, the best guarantees blow up to $O(\log n)$ and $O(\sqrt{n})$. This gap between the two regimes motivates the following question: are there classes of incomplete graphs that circumvent the lower bounds on general graphs and admit approximation guarantees approaching those attainable on complete graphs? We study a natural class of graphs obtained by randomly subsampling a complete signed graph $G$, where each edge is independently deleted with probability $q$. For such graph instances both for the min-max and the min-disagreement objectives, we prove approximation guarantees (depending on $q$) that are substantially better than the bounds achievable for general graphs. We supplement our theoretical results with experiments that also suggest that the approximation ratios of our algorithm are close to those of the complete graph and better than the worst-case bounds for general (non-complete) graphs.

Problem

• Correlation Clustering
• Random Partial Information
• Approximation Guarantees
• Incomplete Graphs

Innovation

• Correlation Clustering
• Random Partial Information
• Approximation Guarantees
• Incomplete Graphs
• Min-Disagreement