Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively represent the complex relations found in high-dimensional data. Such higher-order domains are typically modeled either as hypergraphs, or as simplicial, cubical or other cell complexes. In this context, cell complexes are often seen as a subclass of hypergraphs with additional algebraic structure that can be exploited, e.g., to develop a spectral theory. In this article, we promote an alternative perspective. We argue that hypergraphs and cell complexes emphasize \emph{different} types of relations, which may have different utility depending on the application context. Whereas hypergraphs are effective in modeling set-type, multi-body relations between entities, cell complexes provide an effective means to model hierarchical, interior-to-boundary type relations. We discuss the relative advantages of these two choices and elaborate on the previously introduced concept of a combinatorial complex that enables co-existing set-type and hierarchical relations. Finally, we provide a brief numerical experiment to demonstrate that this modelling flexibility can be advantageous in learning tasks.

图形信号处理技术已成为处理非欧几里德空间中的数据的重要工具，然而，人们越来越意识到这些图形模型可能需要扩展到'高阶'领域，以有效地表示高维数据中的复杂关系。本文提出了一种新的观点，认为超图和细胞复合体强调不同类型的关系，具有不同的应用意义，并介绍了一种组合复合体的概念，以实现并存的集合型和层次关系。最后，通过一个简要的数值实验，展示了这种建模灵活性在学习任务中的优势。

组合复合体: 跨越细胞复合体和超图之间的鸿沟