We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph G whose edges are labeled with + or −, we wish to partition the graph into clusters while trying to avoid errors: + edges between clusters or − edges within clusters. Classically, one seeks to minimize the total number of such errors. We introduce a new framework that allows the objective to be a more general function of the number of errors at each vertex (for example, we may wish to minimize the number of errors at the worst vertex) and provides a rounding algorithm which converts "fractional clusterings" into discrete clusterings while causing only a constant-factor blowup in the number of errors at each vertex. This rounding algorithm yields constant-factor approximation algorithms for the discrete problem under a wide variety of objective functions.
Puleo and Milencovic REF studied a new version of correlation clustering, where the objective was to make sure the maximum number of disagreements on each vertex is minimized.
Correlation Clustering and Biclustering With Locally Bounded Errors
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Computer Science Mathematics