Multi-order hypergraph convolutional networks integrated with self-supervised learning

Hypergraphs, as a powerful representation of information, effectively and naturally depict complex and non-pair-wise relationships in the real world. Hypergraph representation learning is useful for exploring complex relationships implicit in hypergraphs. However, most methods focus on the 1-order neighborhoods and ignore the higher order neighborhood relationships among data on the hypergraph structure. These often result in underutilization of hypergraph structure. In this paper, we exploit the potential of higher order neighborhoods in hypergraphs for representation and propose a Multi-Order Hypergraph Convolutional Network Integrated with Self-supervised Learning. We first encode the multi-channel network of the hypergraph by a high-order spectral convolution operator that captures the multi-order representation of nodes. Then, we introduce an inter-order attention mechanism to preserve the low-order neighborhood information. Finally, to extract valid embedding in the higher order neighborhoods, we incorporate a self-supervised learning strategy based on maximizing mutual information in the multi-order hypergraph convolutional network. Experiments on several hypergraph datasets show that the proposed model is competitive with state-of-the-art baselines, and ablation studies show the effectiveness of higher order neighborhood development, the inter-order attention mechanism, and the self-supervised learning strategy.