Before revision:  These objectives also provide a unifying view of other non-parametric objectives, which often can be captured as special cases. Previous research has largely focused on parametric objectives for standard graphs, in which all nodes are of the same type, and edges model pairwise relationships. In our work, we introduced parameterized objective functions and approximation algorithms specifically for clustering bipartite graphs and hypergraphs, based on correlation clustering. This enables us to develop principled approaches for clustering datasets with different node types (bipartite graphs) or multiway relationships (hypergraphs). Our hypergraph objective is related to higher-order notions of modularity and normalized cut , and is amenable to approximation algorithms via hypergraph expansion techniques.
After revision:  These objectives also provide a unifying view of other non-parametric 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 modularity and normalized cut , and is amenable to approximation algorithms via hypergraph expansion techniques.