  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.
