Clustering Hypergraphs via the MapEquation

A hypergraph is a generalization of graph in that the restriction pairwise affinity scores lifted favor can be evaluated between an arbitrary number inputs. Hypergraphs clustering process finding groups which members given exhibit high similarity and dissimilarity with outside their group. In this paper, we generalize well-known MapEquation, optimization equation used nonhypergraphs, for hypergraphs. We develop agglomerative algorithm, Hypergraph Random Walks (HRW), to find approximate solution generalized MapEquation. Our algorithm requires neither hyperparameter setting nor any on underlying hypergraph. show our has strong theoretical performance newly defined ring hyper cliques demonstrate scales hypergraphs large edge sets.