  Motivated by applications in community detection and dense subgraph
discovery, we consider new clustering objectives in hypergraphs and bipartite
graphs. These objectives are parameterized by one or more resolution parameters
in order to enable diverse knowledge discovery in complex data.
  For both hypergraph and bipartite objectives, we identify parameter regimes
that are equivalent to existing objectives and share their (polynomial-time)
approximation algorithms. We first show that our parameterized hypergraph
correlation clustering objective is related to higher-order notions of
normalized cut and modularity in hypergraphs. It is further amenable to
approximation algorithms via hyperedge expansion techniques.
  Our parameterized bipartite correlation clustering objective generalizes
standard unweighted 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, we highlight a
parameter regime for the bipartite objective where the problem reduces to the
bipartite matching problem and thus can be solved in polynomial time. For other
parameter settings, we present approximation algorithms using linear program
rounding techniques. These results allow us to introduce the first
constant-factor approximation for bicluster deletion, the task of removing a
minimum number of edges to partition a bipartite graph into disjoint
bi-cliques.
  In several experimental results, we highlight the flexibility of our
framework and the diversity of results that can be obtained in different
parameter settings. This includes clustering bipartite graphs across a range of
parameters, detecting motif-rich clusters in an email network and a food web,
and forming clusters of retail products in a product review hypergraph, that
are highly correlated with known product categories.
