High-Speed and Noise-Robust Embedding of Hypergraphs Based on Double-Centered Incidence Matrix

In this study, for the purpose of robust clustering against noise, we propose a fast method of mapping hypernodes and hyperedges onto a unit hypersphere by focusing on the sparsity of the incidence matrix of a hypergraph. Our embedding method quantifies the relative strength of the relationship between a hypernode and a hyperedge from a double-centered incidence matrix, so that the weight of the noisy relationship can be suppressed to a small value, and the influence of noise on the embedding vectors of neighbor nodes and edges can be reduced. From the experimental evaluations using synthetic and real-world hypergraph data, we confirmed that our method outputs clustering results with good accuracy as well as a state-of-the-art method, especially for very noisy hypergraphs, and faster than other compared methods.