Partition graph into complete disjoint subgraphs while maximising sum of edge weights
In addition to Correlation Clustering, this is known as Clique Partitioning or Weighted Cluster Editing, see e.g. 


M. Grötschel and Y. Wakabayashi, A cutting plane algorithm for a clustering problem, or
Sebastian Böcker, Sebastian Briesemeister, and Gunnar W. Klau, Exact Algorithms for Cluster Editing: Evaluation and Experiments.