A nonlinear diffusion method for semi-supervised learning on hypergraphs

TL;DR

This paper introduces a nonlinear diffusion method for semi-supervised learning on hypergraphs, effectively incorporating node features and achieving higher accuracy with faster training compared to existing hypergraph neural networks.

Contribution

It develops a nonlinear hypergraph diffusion process with proven convergence, enabling improved semi-supervised learning by integrating features and labels in a unified framework.

Findings

Outperforms several hypergraph neural networks in accuracy.

Requires less training time than existing methods.

Provides a convergent nonlinear diffusion model with a clear optimization interpretation.

Abstract

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.