Hypergraphs have attracted increasing attention in recent years thanks to their flexibility in naturally modeling a broad range of systems where high-order relationships exist among their interacting ...parts. This survey reviews the newly born hypergraph representation learning problem, whose goal is to learn a function to project objects—most commonly nodes—of an input hyper-network into a latent space such that both the structural and relational properties of the network can be encoded and preserved. We provide a thorough overview of existing literature and offer a new taxonomy of hypergraph embedding methods by identifying three main families of techniques, i.e., spectral, proximity-preserving, and (deep) neural networks. For each family, we describe its characteristics and our insights in a single yet flexible framework and then discuss the peculiarities of individual methods, as well as their pros and cons. We then review the main tasks, datasets, and settings in which hypergraph embeddings are typically used. We finally identify and discuss open challenges that would inspire further research in this field.
Hypergraph Learning: Methods and Practices Gao, Yue; Zhang, Zizhao; Lin, Haojie ...
IEEE transactions on pattern analysis and machine intelligence,
05/2022, Volume:
44, Issue:
5
Journal Article
Peer reviewed
Hypergraph learning is a technique for conducting learning on a hypergraph structure. In recent years, hypergraph learning has attracted increasing attention due to its flexibility and capability in ...modeling complex data correlation. In this paper, we first systematically review existing literature regarding hypergraph generation, including distance-based, representation-based, attribute-based, and network-based approaches. Then, we introduce the existing learning methods on a hypergraph, including transductive hypergraph learning, inductive hypergraph learning, hypergraph structure updating, and multi-modal hypergraph learning. After that, we present a tensor-based dynamic hypergraph representation and learning framework that can effectively describe high-order correlation in a hypergraph. To study the effectiveness and efficiency of hypergraph generation and learning methods, we conduct comprehensive evaluations on several typical applications, including object and action recognition, Microblog sentiment prediction, and clustering. In addition, we contribute a hypergraph learning development toolkit called THU-HyperG.
An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of either +1 or −1. This generalizes signed graphs to a hypergraph setting and simultaneously provides a ...natural definition for a signed adjacency which is used to define the adjacency and Laplacian matrices. Many properties of these matrices are known, but there are no nontrivial families of oriented hypergraphs with their spectrum determined. In this paper we define and study hypergraph families that are analogous to cycles and paths in graphs and signed graphs. The adjacency and Laplacian eigenvalues for some of these families is determined.
Here we introduce connectivity operators, namely, diffusion operators, general Laplacian operators, and general adjacency operators for hypergraphs. These operators are generalisations of some ...conventional notions of apparently different connectivity matrices associated with hypergraphs. In fact, we introduce here a unified framework for studying different variations of the connectivity operators associated with hypergraphs at the same time. Eigenvalues and corresponding eigenspaces of the general connectivity operators associated with some classes of hypergraphs are computed. Applications such as random walks on hypergraphs, dynamical networks, and disease transmission on hypergraphs are studied from the perspective of our newly introduced operators. We also derive spectral bounds for the weak connectivity number, degree of vertices, maximum cut, bipartition width, and isoperimetric constant of hypergraphs.
Traffic Anomaly Detection (TAD) is an important and difficult task in Intelligent Transportation Systems (ITS) . Traffic anomaly events are sparse in both spatial and temporal spaces, posing a ...challenge to the performance of model. Moreover, a single traffic anomaly event can impact multiple road sections in the neighborhood, further undermining the accuracy of TAD. In this paper, we propose a new TAD method based on spatio-temporal hypergraph convolutional neural network. Specifically, we adopt a spatial–temporal augmentation approach for traffic data. This will enhance the performance of detecting sparse anomalies. Meanwhile, we introduce a hypergraph learning method to model the road network. This could capture the spreading features of anomalies for better detection results. Additionally, we design a dynamic hypergraph construction method to extract the evolving relationships of road segments. The proposed model evaluation on the Beijing (SE-BJ) dataset for TAD reveals superior performance compared to state-of-the-art ones.
•Proposed a data augmentation method to enhance the detect effect.•Introduced hypergraph representation for effective road network modeling.•Designed a dynamic hypergraph representation to capture evolving road structures.•Proposed a spatio-temporal hypergraph convolutional network for TAD.
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.
On the spectrum of hypergraphs Banerjee, Anirban
Linear algebra and its applications,
04/2021, Volume:
614
Journal Article
Peer reviewed
Here, we introduce different connectivity matrices and study their eigenvalues to explore various structural properties of a general hypergraph. We investigate how the diameter, connectivity and ...vertex chromatic number of a hypergraph are related to the spectrum of these matrices. Different properties of a regular hypergraph are also characterized by the same. Cheeger constant on a hypergraph is defined and its spectral bounds have been derived for a connected general hypergraph. Random walk on a general hypergraph can also be well studied by analyzing the spectrum of the transition probability operator defined on the hypergraph. We also introduce Ricci curvature on a general hypergraph and study its relation with the hypergraph spectra.
We define notions of a weak homotopy for finite hypergraphs and an exponential hypergraph with a right adjoint to the categorical product of finite hypergraphs, and investigate a connection between ...the weak homotopy and the exponential hypergraph. Then we discuss a Hom construction associated to a pair of finite hypergraphs and prove that the homotopy of hypergraph homomorphisms, defined in (Grigor’Yan et al. in Topol Appl 267:106877, 2019), could be characterized by properties of the Hom construction. In addition, we establish some properties of Hom constructions involving the categorical product of finite hypergraphs. As an application we show that the homotopy of
d
-colorings of a simple hypergraph
H
could be characterized by properties of Hom constructions associated to the maximum simple hypergraph and
H
.
We prove characterizations of the existence of perfect f-matchings in uniform mengerian and perfect hypergraphs. Moreover, we investigate the f-factor problem in balanced hypergraphs. For uniform ...balanced hypergraphs we prove two existence theorems with purely combinatorial arguments, whereas for non-uniform balanced hypergraphs we show that the f-factor problem is NP-hard.
Hypergraph neural networks are widely used in link prediction because of their ability to learn the high-order structure relationship. However, most existing hypergraph modeling relies on the ...attribute information of nodes. And as for the link prediction, missing links are not utilized when training link predictors, so conventional transductive hypergraph learning are generally not consistent with link prediction tasks. To address these limitations, we propose the Network Structure Linear Representation (NSLR) method to model hypergraph for general networks without node attribute information and the inductive hypergraph learning method Hypergraph Multi-view Attention Neural Network (HMANN) that learns the rich high-order structure information from node-level and hyperedge-level. Also, this paper put forwards a novel NSLR-HMANN link prediction algorithm based on NSLR and HMANN methods. Extensive comparison and ablation experiments show that the NSLR-HMANN link prediction algorithm achieves state-of-the-art performance on link prediction and has better performance on robustness.
•The hypergraph modeling method without node information is proposed.•An inductive hypergraph learning method to explore the high-order structure.•We propose a link prediction algorithm using high-order structure information.•Experiments are conducted to verify the advanced performance of the algorithm.
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