摘要：

与节点之间仅具有成对关系的普通网络不同，超网络的节点之间还存在复杂的元组关系，因而现有的大多数普通网络表示学习方法不能有效地捕获复杂的元组关系。为此，提出一种捕获成对关系和元组关系的基于集合约束的异质超网络表示学习方法。结合团扩展和星型扩展，将抽象为超图的异质超网络转化成抽象为2-截图+关联图的异质网络。基于2-截图+关联图，采用感知节点语义相关性的元路径游走方法获取异质节点序列，并通过基于拓扑派生目标函数的模型训练异质节点序列上的成对关系，采用基于集合约束目标函数的模型，将与节点关联的超边集合融入到超网络表示学习中来训练节点之间的元组关系，从而获得高质量的节点表示向量。实验结果表明，对于链接预测任务，该方法的性能接近于其他最优基线方法；对于超网络重建任务，当超边重建比率大于0.7时，该方法在drug数据集上具有较优的性能，在GPS数据集上的平均性能超过其他最优基线方法16.2%。

关键词: 网络表示, 超网络结构, 集合约束, 链接预测, 超网络重建

Abstract:

Unlike ordinary networks, which only have pairwise relationships between the nodes, hypernetworks exhibit more intricate tuple relationships among their nodes. However, most existing representation learning methods for ordinary networks cannot effectively capture such complex tuple relationships. Therefore, this paper proposes a representation learning method for heterogeneous hypernetworks, denoted as Heterogeneous hypernetwork Representation learning with Set Constraints(HRSC), to capture pairwise and tuple relationships. This method combines clique expansion and star expansion to transform a heterogeneous hypernetwork abstracted as a hypergraph into a heterogeneous network abstracted as a 2-section graph+incidence graph. Based on this combination of 2-section graph+incidence graph, the meta-path walk method is employed to consider the semantic relevance of nodes, generating heterogeneous node sequences. Pairwise relationships within these sequences are then trained using a model grounded in topology-derived objective functions. Finally, the model, including a set constraint objective function, incorporates hyperedge sets associated with nodes into the hypernetwork representation learning process to train tuple relationships among nodes, thereby yielding high-quality node representation vectors. Experimental results demonstrate that, for link prediction tasks, the proposed method performs comparably to other optimal baseline methods. In hypernetwork reconstruction tasks, the method outperforms other optimal methods on the drug dataset when the hyperedge reconstruction ratio exceeds 0.7. Additionally, the average performance of the proposed method surpasses other optimal baseline methods by 16.2% on the GPS dataset.

Key words: network representation, hypernetwork structure, set constraint, link prediction, hypernetwork reconstruction