| Autor: |
Hajij, Mustafa, Zamzmi, Ghada, Papamarkou, Theodore, Guzmán-Sáenz, Aldo, Birdal, Tolga, Schaub, Michael T. |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
57th Asilomar Conference on Signals, Systems, and Computers, 2023 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1109/IEEECONF59524.2023.10477018 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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