A nonlinear diffusion method for semi-supervised learning on hypergraphs
This work addresses the challenge of incorporating node features in hypergraph learning, which is important for applications with multiway relationships, but it is incremental as it builds on classical diffusion techniques.
The authors tackled the problem of semi-supervised learning on hypergraphs by developing a nonlinear diffusion method that spreads features and labels, achieving higher accuracy and faster training than existing hypergraph neural networks.
Hypergraphs are a common model for multiway relationships in data, and hypergraph semi-supervised learning is the problem of assigning labels to all nodes in a hypergraph, given labels on just a few nodes. Diffusions and label spreading are classical techniques for semi-supervised learning in the graph setting, and there are some standard ways to extend them to hypergraphs. However, these methods are linear models, and do not offer an obvious way of incorporating node features for making predictions. Here, we develop a nonlinear diffusion process on hypergraphs that spreads both features and labels following the hypergraph structure, which can be interpreted as a hypergraph equilibrium network. Even though the process is nonlinear, we show global convergence to a unique limiting point for a broad class of nonlinearities, which is the global optimum of a interpretable, regularized semi-supervised learning loss function. The limiting point serves as a node embedding from which we make predictions with a linear model. Our approach is much more accurate than several hypergraph neural networks, and also takes less time to train.