In contrast to regular (simple) networks, hyper networks possess the ability to depict more complex relationships among nodes and store extensive information. Such networks are commonly found in real-world applications, such as in social interactions. Learning embedded representations for nodes involves a process that translates network structures into more simplified spaces, thereby enabling the application of machine learning approaches designed for vector data to be extended to network data. Nevertheless, there remains a need to delve into methods for learning embedded representations that prioritize structural aspects. This research introduces HyperS2V, a node embedding approach that centers on the structural similarity within hyper networks. Initially, we establish the concept of hyper-degrees to capture the structural properties of nodes within hyper networks. Subsequently, a novel function is formulated to measure the structural similarity between different hyper-degree values. Lastly, we generate structural embeddings utilizing a multi-scale random walk framework. Moreover, a series of experiments, both intrinsic and extrinsic, are performed on both toy and real networks. The results underscore the superior performance of HyperS2V in terms of both interpretability and applicability to downstream tasks.

翻译：与常规（简单）网络不同，超网络能够描述节点间更复杂的关系并存储丰富信息。这类网络常见于社交互动等现实应用场景。节点嵌入表示学习通过将网络结构映射至简化空间，使得面向向量数据的机器学习方法得以扩展至网络数据。然而，针对优先考虑结构特征的嵌入表示学习方法仍有待深入探索。本研究提出HyperS2V——一种聚焦超网络结构相似性的节点嵌入方法。首先，我们定义超度概念以捕捉超网络中节点的结构属性；其次，构建新型函数度量不同超度值间的结构相似性；最后，通过多尺度随机游走框架生成结构嵌入。此外，我们在模拟网络与真实网络上开展了内在评估与外在评估实验。结果表明，HyperS2V在可解释性及下游任务适用性方面均展现出卓越性能。