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Hypergraph Computation

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This open access book discusses the theory and methods of hypergraph computation.

Many underlying relationships among data can be represented using graphs, for example in the areas including computer vision, molecular chemistry, molecular biology, etc. In the last decade, methods like graph-based learning and neural network methods have been developed to process such data, they are particularly suitable for handling relational learning tasks. In many real-world problems, however, relationships among the objects of our interest are more complex than pair-wise. Naively squeezing the complex relationships into pairwise ones will inevitably lead to loss of information which can be expected valuable for learning tasks. 

Hypergraph, as a generation of graph, has shown superior performance on modelling complex correlations compared with graph. Recent years have witnessed a great popularity of researches on hypergraph-related AI methods, which have been used in computer vision, social media analysis, etc. We summarize these attempts as a new computing paradigm, called hypergraph computation, which is to formulate the high-order correlations underneath the data using hypergraph, and then conduct semantic computing on the hypergraph for different applications. The content of this book consists of hypergraph computation paradigms, hypergraph modelling, hypergraph structure evolution, hypergraph neural networks, and applications of hypergraph computation in different fields. We further summarize recent achievements and future directions on hypergraph computation in this book.

Author(s): Qionghai Dai, Yue Gao
Series: Artificial Intelligence: Foundations, Theory, and Algorithms
Publisher: Springer
Year: 2023

Language: English
Pages: 250
City: Singapore

Preface
Book Organization
Prerequisites
Contact Information
Acknowledgments
Contents
Acronyms
1 Introduction
1.1 Background
1.2 The Definition of Hypergraph
1.3 Applications of Hypergraph
1.4 The History of Studies on Hypergraph
1.4.1 Topology and Coloring on Hypergraph
1.4.2 Hypergraph Partitioning, Clustering, and Machine Learning
1.4.3 Deep Learning on Hypergraph
1.5 Hypergraph Computation: Challenges and Objectives
1.6 Structure of This Book
1.7 Summary
References
2 Mathematical Foundations of Hypergraph
2.1 Introduction
2.2 Preliminary Knowledge of Hypergraph
2.2.1 Undirected Hypergraph
2.2.2 Directed Hypergraph
2.2.3 Probabilistic Hypergraph
2.2.4 K-Uniform Hypergraph
2.2.5 Hypergraph and Bipartite Graph
2.2.6 The Weights on Hypergraph
2.3 Comparison Between Graph and Hypergraph
2.3.1 Low-Order Versus High-Order Correlations
2.3.2 Adjacency Matrix Versus Incidence Matrix
2.3.3 Structure Transformation from Hypergraph to Graph
2.3.4 Random Walks on Graph and Hypergraph
2.4 Summary
References
3 Hypergraph Computation Paradigms
3.1 Introduction
3.2 Intra-hypergraph Computation
3.3 Inter-hypergraph Computation
3.4 Hypergraph Structure Computation
3.5 Summary
References
4 Hypergraph Modeling
4.1 Introduction
4.2 Implicit Hypergraph Modeling
4.2.1 Distance-Based Hypergraph Generation
4.2.2 Representation-Based Hypergraph Generation
4.3 Explicit Hypergraph Modeling
4.3.1 Attribute-Based Hypergraph Generation
4.3.2 Network-Based Hypergraph Generation
4.4 Typical Examples of Hypergraph Modeling
4.4.1 Computer Vision
4.4.2 Recommender System
4.4.3 Computer-Aided Diagnosis
4.4.4 Brain Network
4.5 Hypergraph Modeling in Next Stage
4.5.1 Adaptive Hypergraph Modeling
4.5.2 Generative Hypergraph Modeling
4.5.3 Knowledge Hypergraph Generation
4.6 Summary
References
5 Typical Hypergraph Computation Tasks
5.1 Introduction
5.2 Label Propagation on Hypergraph
5.3 Data Clustering on Hypergraph
5.4 Cost-Sensitive Learning on Hypergraph
(1) Cost-Sensitive Hypergraph Computation
(2) Cost Interval Optimization for Hypergraph Computation
5.5 Link Prediction on Hypergraph
5.6 Summary
References
6 Hypergraph Structure Evolution
6.1 Introduction
6.2 Hypergraph Component Optimization
6.2.1 Hyperedge Weight Optimization
6.2.2 Vertex Weight Optimization
6.2.3 Sub-hypergraph Weight Optimization
6.3 Hypergraph Structure Optimization
6.4 Incremental Learning on Growing Data
6.5 Summary
References
7 Neural Networks on Hypergraph
7.1 Introduction
7.2 Spectral-Based Neural Networks on Hypergraph
7.2.1 Hypergraph Neural Networks
7.2.2 Hypergraph Convolution and Hypergraph Attention
7.2.3 Hyperbolic Hypergraph Neural Networks
7.3 Spatial-Based Neural Networks on Hypergraph
7.3.1 General Hypergraph Neural Networks
7.3.2 Dynamic Hypergraph Neural Networks
7.4 Comparison Between Graph and Hypergraph Neural Networks
7.4.1 Spectral Perspective
7.4.2 Spatial Perspective
7.5 Summary
References
8 Large Scale Hypergraph Computation
8.1 Introduction
8.2 Factorization-Based Big-Hypergraph Modeling
8.3 Hierarchical Hypergraph Modeling
8.4 Summary
References
9 Hypergraph Computation for Social Media Analysis
9.1 Introduction
9.2 Recommender System
9.2.1 Collaborative Filtering
9.2.2 Attribute Inference
9.3 Sentiment Analysis
9.3.1 Sentiment Prediction
9.3.2 Social Event Detection
9.4 Emotion Recognition
9.5 Summary
References
10 Hypergraph Computation for Medical and Biological Applications
10.1 Introduction
10.2 Computer-Aided Diagnosis
10.2.1 MCI Identification Using MRI
10.2.2 Medical Image Retrieval
10.2.3 COVID-19 Identification Using CT Imaging
10.2.4 ASD Identification Using Brain Functional Networks
10.3 Survival Prediction with Histopathological Image
10.3.1 Ranking-Based Survival Prediction
10.3.2 Phenotypic and Topological Hypergraph Modeling
10.4 Drug Discovery
10.5 Medical Image Segmentation
10.6 Summary
References
11 Hypergraph Computation for Computer Vision
11.1 Introduction
11.2 Visual Classification
11.3 3D Object Retrieval
11.4 Tag-Based Social Image Retrieval
11.5 Summary
References
12 The DeepHypergraph Library
12.1 Introduction
12.2 The Correlation Structures in DHG
12.3 The Function Library in DHG
12.4 Summary
References
13 Conclusions and Future Work
13.1 Summary of This Book
13.2 Future Work