Before revision:  Our bipartite objective generalizes standard  bipartite correlation clustering, and in a certain parameter regime is equivalent to bicluster deletion, i. e., removing a minimum number of edges to separate a bipartite graph into disjoint bicliques. The problem in general is NP-hard, but we show that in a certain parameter regime it is equivalent to a bipartite matching problem , meaning that it is polynomial timesolvable in this regime .
After revision:  Our bipartite objective generalizes standard bipartite correlation clustering, as well as bicluster deletion. For a certain choice of parameters it is also related to our hypergraph objective. Although in general it is NP-hard, but we show that in a certain parameter regime it is equivalent to a bipartite matching problem , meaning that it is polynomial timesolvable in this regime .