Titlebook: Hypergraph Computation; Qionghai Dai,Yue Gao Book‘‘‘‘‘‘‘‘ 2023 The Editor(s) (if applicable) and The Author(s) 2023 Hypergraph.Hypergraph

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Introduction,lationship between two subjects, hypergraph is a flexible and representative model to formulate high-order correlations. Based on the hypergraph model, there have been many efforts to design the computation framework and analyze the high-order correlations. In this chapter, we briefly introduce the

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Mathematical Foundations of Hypergraph,standing and analysis of hypergraph structure. A hypergraph is composed of a set of vertices and hyperedges, and it is a generalization of a graph, where a weighted hypergraph quantifies the relative importance of hyperedges or vertices. Hypergraph can also be divided into two main categories, i.e.,

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Hypergraph Computation Paradigms,tructure computation. Intra-hypergraph computation representation aims to conduct representation learning of a hypergraph, where each subject is represented by a hypergraph of its components. Inter-hypergraph computation is to conduct representation learning of vertices in the hypergraph, where each

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Hypergraph Modeling, formulate the high-order correlation among data. In this section, we introduce different hypergraph modeling methods to show how to build hypergraphs using various pieces of information, such as features, attributes, and/or graphs. These methods are organized into two broad categories, depending on

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Typical Hypergraph Computation Tasks,r typical hypergraph computation tasks, including label propagation, data clustering, imbalance learning, and link prediction. The first typical task is label propagation, which is to predict the labels for the vertices, i.e., assigning a label to each unlabeled vertex in the hypergraph, based on th

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Hypergraph Structure Evolution,troduced into the generated hypergraph structure, which may lead to inaccurate inference on hypergraph. Another issue comes from the increasing data stream, which is also very common in many applications. It is important to consider the structure evolution methods on the hypergraph, which optimize t