HGT: Transformer Architecture for Arbitrary Hypergraphs Based on P-Laplacian

In the real world, many complex relationship networks are better represented as hypergraphs, such as social networks and EDA netlists. Traditional graph neural networks struggle to capture the high-order relationships expressed by hyperedges, resulting in a loss of structure information. Transformer models can be adapted to run on fully connected graph neural networks. Unfortunately, this architecture ignores the inherent connectivity induction bias of hypergraphs and fails to capture the relative positional relationships between hyper-nodes and hyperedges. Therefore, the challenge in hypergraph representation learning is how to capture the more complex and unique structural information of hypergraphs while ensuring the stability of the model. To address this issue, we propose the Hypergraph Transformer model (HGT), a general Transformer model capable of extracting hypergraph node embeddings while preserving rich structural information. In HGT, we introduce p*-Laplacian operator and HSPD algorithm. We assign a p*-Laplacian eigenvector as the positional encoding for each node by a neat way and design the HSPD algorithm to extract the hyperedge structural information in advance. To enhance the hypergraph representation capability of HGT, we incorporate the shortest path feature through the hyperedge into the computation of attention coefficients between nodes. Finally, we conduct extensive multidimensional experiments on HGT. The results validate that our approach does not increase the time complexity compared with the traditional p-Laplacian operator, while surpassing it across multiple indicators in downstream tasks, such as node classification, improving accuracy by 3% to 5%.