Practical real-world scenarios such as the Internet, social networks, and biological networks present the challenges of data scarcity and complex correlations, which limit the applications of artificial intelligence. The graph structure is a typical tool used to formulate such correlations, it is incapable of modeling high-order correlations among different objects in systems; thus, the graph structure cannot fully convey the intricate correlations among objects. Confronted with the aforementioned two challenges, hypergraph computation models high-order correlations among data, knowledge, and rules through hyperedges and leverages these high-order correlations to enhance the data. Additionally, hypergraph computation achieves collaborative computation using data and high-order correlations, thereby offering greater modeling flexibility. In particular, we introduce three types of hypergraph computation methods: ① hypergraph structure modeling, ② hypergraph semantic computing, and ③ efficient hypergraph computing. We then specify how to adopt hypergraph computation in practice by focusing on specific tasks such as three-dimensional (3D) object recognition, revealing that hypergraph computation can reduce the data requirement by 80% while achieving comparable performance or improve the performance by 52% given the same data, compared with a traditional data-based method. A comprehensive overview of the applications of hypergraph computation in diverse domains, such as intelligent medicine and computer vision, is also provided. Finally, we introduce an open-source deep learning library, DeepHypergraph (DHG), which can serve as a tool for the practical usage of hypergraph computation.

中文翻译：

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 超图计算


互联网、社交网络和生物网络等实际场景面临数据稀缺和复杂关联的挑战，这限制了人工智能的应用。图结构是用于表述此类关联的典型工具，它无法对系统中不同对象之间的高阶关联进行建模；因此，图结构无法完全表达对象之间错综复杂的相关性。面对上述两个挑战，超图计算通过超边对数据、知识和规则之间的高阶相关性进行建模，并利用这些高阶相关性来增强数据。此外，超图计算利用数据和高阶相关性实现协作计算，从而提供更大的建模灵活性。我们特别介绍了三类超图计算方法：①超图结构建模，②超图语义计算，③高效超图计算。然后，我们通过关注三维 (3D) 对象识别等特定任务来具体说明如何在实践中采用超图计算，揭示超图计算可以在实现可比性能的同时将数据需求减少 80%，或者在给定的情况下将性能提高 52%与传统的基于数据的方法相比，相同的数据。还全面概述了超图计算在智能医学和计算机视觉等不同领域的应用。最后，我们介绍一个开源深度学习库 DeepHypergraph (DHG)，它可以作为超图计算实际使用的工具。