LP-Based Pivoting Algorithm for Higher-Order Correlation Clustering

Correlation clustering is an approach for clustering a set of objects from given pairwise information. In this approach, the given pair-wise information is usually represented by an undirected graph with nodes corresponding to the objects, where each edge in the graph is assigned a nonnegative weight, and either the positive or negative label. Then, a clustering is obtained by solving an optimization problem of finding a partition of the node set that minimizes the disagreement or maximizes the agreement with the pairwise information. In this paper, we extend correlation clustering with disagreement minimization to deal with higher-order relationships represented by hypergraphs. We give two pivoting algorithms based on a linear programming relaxation of the problem. One achieves an O(k log n)-approximation, where n is the number of nodes and k is the maximum size of hyperedges with the negative labels. This algorithm can be applied to any hyperedges with arbitrary weights. The other is an O(r)-approximation for complete r-partite hypergraphs with uniform weights. This type of hypergraphs arise from the coclustering setting of correlation clustering.