Hypergraph clustering with inhomogeneous partitions of hyperedges

The extension of conventional clustering to hypergraph clustering, which involves higher order relations among nodes instead of pairwise relations, is increasingly gaining attention, as multi-node relations may capture more informative clustering structures. One of widely used methodologies for hypergraph clustering is to minimize a normalized sum of the costs to partition hyperedges across clusters. All the approaches along this line were proposed by assuming that different types of partitioning of one hyperedge correspond to one single cost. However, this assumption limits the usage of hypergraph clustering because of the failure to leverage the possible non-uniformity of hyperedges. In this paper, we proposed a hypergraph clustering approach that can handle non-uniform partitioning costs assigned to hyperedges. We first prove that the algorithm can achieve a quadratically approximate solution if the non-uniform costs satisfy some soft conditions. Moreover, we list some applications in ranking data analysis, subspace segmentation and network structure analysis, where, by allowing non-uniform partition of hyperedges, our algorithm outperforms traditional hypergraph clustering methods.