Previous hypergraph expansions are solely carried out on either vertex level or hyperedge level, thereby missing the symmetric nature of data co-occurrence, and resulting in information loss. To address the problem, this paper treats vertices and hyperedges equally and proposes a new hypergraph formulation named the \emph{line expansion (LE)} for hypergraphs learning. The new expansion bijectively induces a homogeneous structure from the hypergraph by treating vertex-hyperedge pairs as "line nodes". By reducing the hypergraph to a simple graph, the proposed \emph{line expansion} makes existing graph learning algorithms compatible with the higher-order structure and has been proven as a unifying framework for various hypergraph expansions. We evaluate the proposed line expansion on five hypergraph datasets, the results show that our method beats SOTA baselines by a significant margin.

翻译：以往的超图展开仅在顶点层面或超边层面进行，从而忽略了数据共现的对称性，导致信息损失。为解决该问题，本文平等对待顶点和超边，提出了一种新的超图表示形式——线展开（line expansion），用于超图学习。该新展开通过将顶点-超边对视为"线节点"，从超图双射地诱导出同质结构。通过将超图简化为简单图，所提出的线展开使现有图学习算法能够兼容高阶结构，并已被证明是多种超图展开的统一框架。我们在五个超图数据集上评估了所提出的线展开方法，结果表明我们的方法以显著优势超越了当前最先进的基线模型。