Modularity-based Hypergraph Clustering: Random Hypergraph Model, Hyperedge-cluster Relation, and Computation.

A graph models the connections among objects. One important graph analytical task is clustering which partitions a data graph into clusters with dense innercluster connections. A line of clustering maximizes a function called modularity. Modularity-based clustering is widely adopted on dyadic graphs due to its scalability and clustering quality which depends highly on its selection of a random graph model. The random graph model decides not only which clustering is preferred - modularity measures the quality of a clustering based on its alignment to the edges of a random graph, but also the cost of computing such an alignment. Existing random hypergraph models either measure the hyperedge-cluster alignment in an All-Or-Nothing (AON) manner, losing important group-wise information, or introduce expensive alignment computation, refraining the clustering from scaling up. This paper proposes a new random hypergraph model called Hyperedge Expansion Model (HEM), a non-AON hypergraph modularity function called Partial Innerclusteredge modularity (PI) based on HEM, a clustering algorithm called Partial Innerclusteredge Clustering (PIC) that optimizes PI, and novel computation optimizations. PIC is a scalable modularity-based hypergraph clustering that can effectively capture the non-AON hyperedge-cluster relation. Our experiments show that PIC outperforms eight state-of-the-art methods on real-world hypergraphs in terms of both clustering quality and scalability and is up to five orders of magnitude faster than the baseline methods.