Bounding and Comparing Methods for Correlation Clustering Beyond ILP

We evaluate several heuristic solvers for correlation clustering, the NP-hard problem of partitioning a dataset given pairwise affinities between all points. We experiment on two practical tasks, document clustering and chat disentanglement, to which ILP does not scale. On these datasets, we show that the clustering objective often, but not always, correlates with external metrics, and that local search always improves over greedy solutions. We use semi-definite programming (SDP) to provide a tighter bound, showing that simple algorithms are already close to optimality.