Hypergraph Structure Inference From Data Under Smoothness Prior

Hypergraphs are important for processing data with higher-order relationships involving more than two entities. In scenarios where explicit hypergraphs are not readily available, it is desirable to infer a meaningful hypergraph structure from the node features to capture the intrinsic relations within the data. However, existing methods either adopt simple pre-defined rules that fail to precisely capture the distribution of the potential hypergraph structure, or learn a mapping between hypergraph structures and node features but require a large amount of labelled data, i.e., pre-existing hypergraph structures, for training. Both restrict their applications in practical scenarios. To fill this gap, we propose a novel smoothness prior that enables us to design a method to infer the probability for each potential hyperedge without labelled data as supervision. The proposed prior indicates features of nodes in a hyperedge are highly correlated by the features of the hyperedge containing them. We use this prior to derive the relation between the hypergraph structure and the node features via probabilistic modelling. This allows us to develop an unsupervised inference method to estimate the probability for each potential hyperedge via solving an optimisation problem that has an analytical solution. Experiments on both synthetic and real-world data demonstrate that our method can learn meaningful hypergraph structures from data more efficiently than existing hypergraph structure inference methods.