Before revision:  First of all, we demonstrate how to incorporate recent results on generalized hypergraph s-t cut problems . This allows us to accommodate a wide range of different hypergraph cut functions, which can assign different penalties based on how each hyperedgeis split across different clusters. Furthermore, our algorithm comes with a number of attractive theoretical properties in terms of recovering nodes sets with low hypergraph conductance and hypergraph normalized cut scores.
After revision:  First of all, we demonstrate how to incorporate recent results on generalized hypergraph s-t cut problems in order to identify a nearby well-connected cluster of nodes that overlaps substantially with the input set. Our methods extend graph-based techniques but are significantly more general and have new output quality guarantees. First, our methods can minimize new generalized notions of hypergraph cuts, which depend on specific configurations of nodes within each hyperedge, rather than just on the number of cut hyperedges. Second, our framework has several attractive theoretical properties in terms of recovering nodes sets with low hypergraph conductance and hypergraph normalized cut scores.