Improved Theoretical and Practical Guarantees for Chromatic Correlation Clustering

We study a natural generalization of the correlation cluster-ing problem to graphs in which the pairwise relations be-tween objects are categorical instead of binary. This prob-lem was recently introduced by Bonchi et al. under the name of chromatic correlation clustering, and is motivated by many real-world applications in data-mining and social networks, including community detection, link classification, and entity de-duplication. Our main contribution is a fast and easy-to-implement constant approximation framework for the problem, which builds on a novel reduction of the problem to that of cor-relation clustering. This result significantly progresses the current state of knowledge for the problem, improving on a previous result that only guaranteed linear approximation in the input size. We complement the above result by devel-oping a linear programming-based algorithm that achieves an improved approximation ratio of 4. Although this al-gorithm cannot be considered to be practical, it further ex-tends our theoretical understanding of chromatic correlation clustering. We also present a fast heuristic algorithm that is motivated by real-life scenarios in which there is a ground-truth clustering that is obscured by noisy observations. We test our algorithms on both synthetic and real datasets, like social networks data. Our experiments reinforce the theoret-ical findings by demonstrating that our algorithms generally outperform previous approaches, both in terms of solution cost and reconstruction of an underlying ground-truth clus-tering