Hypergraph Structure Research Articles

HyperTMO: a trusted multi-omics integration framework based on hypergraph convolutional network for patient classification.

The rapid development of high-throughput biomedical technologies can provide researchers with detailed multi-omics data. The multi-omics integrated analysis approach based on machine learning contributes a more comprehensive perspective to human disease research. However, there are still significant challenges in representing single-omics data and integrating multi-omics information. This article presents HyperTMO, a Trusted Multi-Omics integration framework based on Hypergraph convolutional network for patient classification. HyperTMO constructs hypergraph structures to represent the association between samples in single-omics data, then evidence extraction is performed by hypergraph convolutional network, and multi-omics information is integrated at an evidence level. Last, we experimentally demonstrate that HyperTMO outperforms other state-of-the-art methods in breast cancer subtype classification and Alzheimer's disease classification tasks using multi-omics data from TCGA (BRCA) and ROSMAP datasets. Importantly, HyperTMO is the first attempt to integrate hypergraph structure, evidence theory, and multi-omics integration for patient classification. Its accurate and robust properties bring great potential for applications in clinical diagnosis. HyperTMO and datasets are publicly available at https://github.com/ippousyuga/HyperTMO.

Finite-Time Frequentist Regret Bounds of Multi-Agent Thompson Sampling on Sparse Hypergraphs

We study the multi-agent multi-armed bandit (MAMAB) problem, where agents are factored into overlapping groups. Each group represents a hyperedge, forming a hypergraph over the agents. At each round of interaction, the learner pulls a joint arm (composed of individual arms for each agent) and receives a reward according to the hypergraph structure. Specifically, we assume there is a local reward for each hyperedge, and the reward of the joint arm is the sum of these local rewards. Previous work introduced the multi-agent Thompson sampling (MATS) algorithm and derived a Bayesian regret bound. However, it remains an open problem how to derive a frequentist regret bound for Thompson sampling in this multi-agent setting. To address these issues, we propose an efficient variant of MATS, the epsilon-exploring Multi-Agent Thompson Sampling (eps-MATS) algorithm, which performs MATS exploration with probability epsilon while adopts a greedy policy otherwise. We prove that eps-MATS achieves a worst-case frequentist regret bound that is sublinear in both the time horizon and the local arm size. We also derive a lower bound for this setting, which implies our frequentist regret upper bound is optimal up to constant and logarithm terms, when the hypergraph is sufficiently sparse. Thorough experiments on standard MAMAB problems demonstrate the superior performance and the improved computational efficiency of eps-MATS compared with existing algorithms in the same setting.

Dual-view hypergraph attention network for news recommendation

News Recommendation (NR) helps users to quickly find their mostly interested information. Recently, some NR systems based on graph neural networks has achieved significant performance improvement in that they use a graph structure to pair-wisely link two nodes (e.g., user, news, topic node) for representation learning. However, such kind of pairwise edges may be not enough to describe multifaceted relations involving more than two nodes; While a hypergraph structure with one hyperedge connecting two and more nodes might be a better choice. Considering this, we propose a dual-view hypergraph attention network for news recommendations (Hyper4NR) in this paper. In particular, we design a dual-view hypergraph structure to model users’ click history, containing both topic-view hyperedges and semantic-view hyperedges. On the constructed hypergraph, we use hyperedge-specific attention network (HSAN) to pass messages in between hyperedges and nodes to encode their representations based on a self-supervised learning approach. Furthermore, we construct another kind of candidate hypergraph on which we apply the HyperGAT to obtain enhanced candidate news encoding. Extensive experiments on the widely used MIND news dataset and Adressa dataset show that our Hyper4NR outperforms these state-of-the-art NR methods.

Online multi-hypergraph fusion learning for cross-subject emotion recognition

Multimodal fusion for emotion recognition has received increasing attention from researchers because of its ability to effectively leverage multimodal complementary information. However, there are two main challenges lead to performance degradation of existing emotion recognition models, which limits the practical use of existing models. One is that multimodal signals are difficult to fuse effectively to respond to the complexity of emotions. The other is that the individual variability and non-stationarity of physiological signals lead to poor performance of the model on new subjects. In particular, existing methods will not work well when faced with emotion recognition of new subjects in online scenarios. In this paper, we propose a novel online multi-hypergraph fusion learning method (OnMHF) to effectively fuse multimodal information and to reduce the difference between training data and test data for online cross-subject emotion recognition. Specifically, in a training phase, a multi-hypergraph fusion is proposed to fuse multimodal physiological signals to effectively obtain emotion-aware information via leveraging multimodal complementary information and high-order correlations among multimodal signals. In an online recognizing phase, an online multi-hypergraph learning is designed to learn online multimodal information from online multimodal data by updating hypergraph structure. As a result, the proposed method can be more effective for emotion recognition of target subjects when target data arrive in an online manner. Experimental results have demonstrated that the proposed method outperforms the baselines and compared state-of-the-art methods in online emotion recognition tasks.

Privacy-Preserving Individual-Level COVID-19 Infection Prediction via Federated Graph Learning

Accurately predicting individual-level infection state is of great value since its essential role in reducing the damage of the epidemic. However, there exists an inescapable risk of privacy leakage in the fine-grained user mobility trajectories required by individual-level infection prediction. In this article, we focus on developing a framework of privacy-preserving individual-level infection prediction based on federated learning (FL) and graph neural networks (GNN). We propose Falcon , a F ederated gr A ph L earning method for privacy-preserving individual-level infe C tion predicti ON . It utilizes a novel hypergraph structure with spatio-temporal hyperedges to describe the complex interactions between individuals and locations in the contagion process. By organically combining the FL framework with hypergraph neural networks, the information propagation process of the graph machine learning is able to be divided into two stages distributed on the server and the clients, respectively, so as to effectively protect user privacy while transmitting high-level information. Furthermore, it elaborately designs a differential privacy perturbation mechanism as well as a plausible pseudo location generation approach to preserve user privacy in the graph structure. Besides, it introduces a cooperative coupling mechanism between the individual-level prediction model and an additional region-level model to mitigate the detrimental impacts caused by the injected obfuscation mechanisms. Extensive experimental results show that our methodology outperforms state-of-the-art algorithms and is able to protect user privacy against actual privacy attacks. Our code and datasets are available at the link: https://github.com/wjfu99/FL-epidemic .

A novel complex-high-order graph convolutional network paradigm: ChyGCN

Abstract In recent years, there has been a growing interest in Graph Convolutional Networks (GCN). However, existing GCN and variants are predominantly based on simple graph or hypergraph structures, which restricts their ability to handle complex data correlations in practical applications. These limitations stem from the difficulty in establishing multiple hierarchies and acquiring adaptive weights for each of them. To address this issue, this paper introduces the latest concept of complex hypergraphs and constructs a versatile high-order multi-level data correlation model. This model is realized by establishing a three-tier structure of complexes-hypergraphs-vertices. Specifically, we start by establishing hyperedge clusters on the foundational network, utilizing a second-order hypergraph structure to depict potential correlations. For this second-order structure, truncation methods are applied to assess and generate a three-layer composite structure. During the construction of the composite structure, an adaptive learning strategy is implemented to merge correlations across different levels. We evaluate this model on several popular datasets and compare it with recent state-of-the-art methods. The comprehensive assessment results demonstrate that the proposed model surpasses existing methods, particularly in modeling implicit data correlations (the classification accuracy of nodes on five public datasets Cora, Citeseer, Pubmed, Github Web ML, and Facebook is 86.1±0.33, 79.2±0.35, 83.1±0.46, 83.8±0.23, and 80.1±0.37, respectively). This indicates that our approach holds advantages when handling datasets with implicit multi-level structures.

Dynamic Hypergraph Structure Learning for Multivariate Time Series Forecasting

Dynamic Hypergraph Structure Learning for Multivariate Time Series Forecasting

Geometric Aspects of Observability of Hypergraphs

In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in many real-world networks including those that arise in biology. We consider polynomial dynamical systems with linear outputs defined according to hypergraph structure, and we propose methods to evaluate local, weak observability.

DHM-Net: Deep Hypergraph Modeling for Robust Feature Matching.

We present a novel deep hypergraph modeling architecture (called DHM-Net) for feature matching in this paper. Our network focuses on learning reliable correspondences between two sets of initial feature points by establishing a dynamic hypergraph structure that models group-wise relationships and assigns weights to each node. Compared to existing feature matching methods that only consider pair-wise relationships via a simple graph, our dynamic hypergraph is capable of modeling nonlinear higher-order group-wise relationships among correspondences in an interaction capturing and attention representation learning fashion. Specifically, we propose a novel Deep Hypergraph Modeling block, which initializes an overall hypergraph by utilizing neighbor information, and then adopts node-to-hyperedge and hyperedge-to-node strategies to propagate interaction information among correspondences while assigning weights based on hypergraph attention. In addition, we propose a Differentiation Correspondence-Aware Attention mechanism to optimize the hypergraph for promoting representation learning. The proposed mechanism is able to effectively locate the exact position of the object of importance via the correspondence aware encoding and simple feature gating mechanism to distinguish candidates of inliers. In short, we learn such a dynamic hypergraph format that embeds deep group-wise interactions to explicitly infer categories of correspondences. To demonstrate the effectiveness of DHM-Net, we perform extensive experiments on both real-world outdoor and indoor datasets. Particularly, experimental results show that DHM-Net surpasses the state-of-the-art method by a sizable margin. Our approach obtains an 11.65% improvement under error threshold of 5° for relative pose estimation task on YFCC100M dataset. Code will be released at https://github.com/CSX777/DHM-Net.

Multi-View Time-Series Hypergraph Neural Network for Action Recognition.

Recently, action recognition has attracted considerable attention in the field of computer vision. In dynamic circumstances and complicated backgrounds, there are some problems, such as object occlusion, insufficient light, and weak correlation of human body joints, resulting in skeleton-based human action recognition accuracy being very low. To address this issue, we propose a Multi-View Time-Series Hypergraph Neural Network (MV-TSHGNN) method. The framework is composed of two main parts: the construction of a multi-view time-series hypergraph structure and the learning process of multi-view time-series hypergraph convolutions. Specifically, given the multi-view video sequence frames, we first extract the joint features of actions from different views. Then, limb components and adjacent joints spatial hypergraphs based on the joints of different views at the same time are constructed respectively, temporal hypergraphs are constructed joints of the same view at continuous times, which are established high-order semantic relationships and cooperatively generate complementary action features. After that, we design a multi-view time-series hypergraph neural network to efficiently learn the features of spatial and temporal hypergraphs, and effectively improve the accuracy of skeleton-based action recognition. To evaluate the effectiveness and efficiency of MV-TSHGNN, we conduct experiments on NTU RGB+D, NTU RGB+D 120 and imitating traffic police gestures datasets. The experimental results indicate that our proposed method model achieves the new state-of-the-art performance.

Adaptive Neural Message Passing for Inductive Learning on Hypergraphs.

Graphs are the most ubiquitous data structures for representing relational datasets and performing inferences in them. They model, however, only pairwise relations between nodes and are not designed for encoding the higher-order relations. This drawback is mitigated by hypergraphs, in which an edge can connect an arbitrary number of nodes. Most hypergraph learning approaches convert the hypergraph structure to that of a graph and then deploy existing geometric deep learning methods. This transformation leads to information loss, and sub-optimal exploitation of the hypergraph's expressive power. We present HyperMSG, a novel hypergraph learning framework that uses a modular two-level neural message passing strategy to accurately and efficiently propagate information within each hyperedge and across the hyperedges. HyperMSG adapts to the data and task by learning an attention weight associated with each node's degree centrality. Such a mechanism quantifies both local and global importance of a node, capturing the structural properties of a hypergraph. HyperMSG is inductive, allowing inference on previously unseen nodes. Further, it is robust and outperforms state-of-the-art hypergraph learning methods on a wide range of tasks and datasets. Finally, we demonstrate the effectiveness of HyperMSG in learning multimodal relations through detailed experimentation on a challenging multimedia dataset.

A Cooperative Dynamic Game via Hypergraph Distributed Optimization

We propose a novel cooperative dynamic game with the use of distributed optimization methods. Each coalition has an objective function and the goal of all the coalitions is to optimize the summation of their objectives given the interactions of their agents. The internal interactions are described by a multigraph but we will use directly a stochastic matrix to describe them while the external interactions are described by a hypergraph. The objective functions are quadratic and they encompass information for both types of interactions to highlight their importance in the outcome for the coalitions. The problem is formulated by means of distributed optimization where the actions of the agents at each iteration are the optimum solutions of the sequential optimization problem and the game is evolving by using a tilted matrix mechanism. We show that the optimization problem at each iteration can be solved in one step via a dual decomposition algorithm by exploiting the hypergraph structure of the optimization problem. For the complete description of the dynamic game we propose a switched dynamical system and we demonstrate its convergence numerically.

Dimensionality reduction of rotor fault dataset based on joint embedding of multi-class graphs

Traditional dimensionality reduction techniques usually rely on a single or a limited number of similar graphs for graph embedding, which limits their ability to extract more information about the internal structure of the data. To address this problem, this study proposes a rotor fault dataset dimensionality reduction algorithm based on multi-class graph joint embedding (MCGJE). The algorithm first overcomes the defect that the traditional feature space cannot take both local and global information into account by constructing local and global median feature line graphs; secondly, based on the graph embedding framework, the algorithm also constructs a hypergraph structure for inscribing complex multivariate relationships between high-dimensional data in the feature space, which in turn enables it to contain more fault information. Finally, we conducted two different rotor fault simulation experiments. The results show that the MCGJE-based algorithm has robust dimensionality reduction capability and can significantly improve the accuracy of fault identification.

Unveiling the potential of long-range dependence with mask-guided structure learning for hypergraph

Hypergraph neural networks have recently drawn widespread attention and have succeeded in many fields. However, existing hypergraph-based neural network approaches are limited to learning local neighborhoods and ignore the representation of long-range dependence. Since the lack of necessary long-range interactions tends to lose critical signals from distant nodes, this paper proposes a new mask-guided hypergraph structure learning (MHSL) method. Specifically, MHSL is comprised of two learning components, i.e., the structure learning component and the initial hypergraph learning component. We design a flexible hypergraph structure learning module in the structure learning component to generate a hypergraph representing the global structure by node stream and hyperedge stream. The initial hypergraph learning component contains the hypergraph convolution that retains the local topological information. Additionally, we design a bidirectional node and hyperedge contrastive learning to learn the consistency between local and global structures. The node classification experiments on the hypergraph datasets demonstrate that the proposed MHSL method achieves competitive performance.

A Distributed Block-Split Gibbs Sampler with Hypergraph Structure for High-Dimensional Inverse Problems

Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods hardly scale to high dimensional problems, they have recently been paired with optimization techniques, such as proximal and splitting approaches, to address this issue. Such approaches pave the way to distributed samplers, splitting computations to make inference more scalable and faster. We introduce a distributed Split Gibbs sampler (SGS) to efficiently solve such problems involving distributions with multiple smooth and non-smooth functions composed with linear operators. The proposed approach leverages a recent approximate augmentation technique reminiscent of primal-dual optimization methods. It is further combined with a block-coordinate approach to split the primal and dual variables into blocks, leading to a distributed block-coordinate SGS. The resulting algorithm exploits the hypergraph structure of the involved linear operators to efficiently distribute the variables over multiple workers under controlled communication costs. It accommodates several distributed architectures, such as the Single Program Multiple Data and client-server architectures. Experiments on a large image deblurring problem show the performance of the proposed approach to produce high quality estimates with credibility intervals in a small amount of time. Supplementary material to reproduce the experiments is available online.

Hypergraph analysis based on a compatible tensor product structure

We propose a tensor product structure that is compatible with the hypergraph structure. We define the algebraic connectivity of the (m+1)-uniform hypergraph in this product, and prove the relationship with the vertex connectivity. We introduce some connectivity optimization problem into the hypergraph, and solve them with the algebraic connectivity. We introduce the Laplacian eigenmap algorithm to the hypergraph under our tensor product.

Prediction of multi-relational drug-gene interaction via Dynamic hyperGraph Contrastive Learning.

Drug-gene interaction prediction occupies a crucial position in various areas of drug discovery, such as drug repurposing, lead discovery and off-target detection. Previous studies show good performance, but they are limited to exploring the binding interactions and ignoring the other interaction relationships. Graph neural networks have emerged as promising approaches owing to their powerful capability of modeling correlations under drug-gene bipartite graphs. Despite the widespread adoption of graph neural network-based methods, many of them experience performance degradation in situations where high-quality and sufficient training data are unavailable. Unfortunately, in practical drug discovery scenarios, interaction data are often sparse and noisy, which may lead to unsatisfactory results. To undertake the above challenges, we propose a novel Dynamic hyperGraph Contrastive Learning (DGCL) framework that exploits local and global relationships between drugs and genes. Specifically, graph convolutions are adopted to extract explicit local relations among drugs and genes. Meanwhile, the cooperation of dynamic hypergraph structure learning and hypergraph message passing enables the model to aggregate information in a global region. With flexible global-level messages, a self-augmented contrastive learning component is designed to constrain hypergraph structure learning and enhance the discrimination of drug/gene representations. Experiments conducted on three datasets show that DGCL is superior to eight state-of-the-art methods and notably gains a 7.6% performance improvement on the DGIdb dataset. Further analyses verify the robustness of DGCL for alleviating data sparsity and over-smoothing issues.

RETRACTED: A Global Structural Hypergraph Convolutional Model for Bundle Recommendation

Bundle recommendations provide personalized suggestions to users by combining related items into bundles, aiming to enhance users’ shopping experiences and boost merchants’ sales revenue. Existing solutions based on graph neural networks (GNN) face several significant challenges: (1) it is demanding to explicitly model multiple complex associations using standard graph neural networks, (2) numerous additional nodes and edges are introduced to approximate higher-order associations, and (3) the user–bundle historical interaction data are highly sparse. In this work, we propose a global structural hypergraph convolutional model for bundle recommendation (SHCBR) to address the above problems. Specifically, we jointly incorporate multiple complex interactions between users, items, and bundles into a relational hypergraph without introducing additional nodes and edges. The hypergraph structure inherently incorporates higher-order associations, thereby alleviating the training burden on neural networks and the dilemma of scarce data effectively. In addition, we design a special matrix propagation rule that captures non-pairwise complex relationships between entities. Using item nodes as links, structural hypergraph convolutional networks learn representations of users and bundles on a relational hypergraph. Experiments conducted on two real-world datasets demonstrate that the SHCBR outperforms the state-of-the-art baselines by 11.07–25.66% on Recall and 16.81–33.53% on NDCG. Experimental results further indicate that the approach based on hypergraphs can offer new insights for addressing bundle recommendation challenges. The codes and datasets have been publicly released on GitHub.

Explainable and programmable hypergraph convolutional network for imaging genetics data fusion

Integrating multi-view information to gain a new understanding of complex disease like Alzheimer’s disease (AD) has great clinical value. Hypergraphs have unique advantages in modeling high-order associations, but current deep learning methods cannot fully utilize the structural information in hypergraphs and have limited application value due to the black-box nature. This paper improves the hypergraph learning in interpretability and programmability. Firstly, we fuse multi-view information by constructing brain region-gene hypergraphs. Secondly, a characteristic information aggregation model is constructed based on hypergraph structure, Finally, a characteristic information aggregation hypergraph convolutional network (CIA-HGCN) is proposed based on the idea of graph neural networks. Evaluated by clinical imaging genetics data, CIA-HGCN obtained accuracy of 88.3% in AD identification task and showed superior performance in characteristic extraction. This paper provides a practical and flexible deep learning method for AD research and clinical applications.

Reconstructing particles in jets using set transformer and hypergraph prediction networks

The task of reconstructing particles from low-level detector response data to predict the set of final state particles in collision events represents a set-to-set prediction task requiring the use of multiple features and their correlations in the input data. We deploy three separate set-to-set neural network architectures to reconstruct particles in events containing a single jet in a fully-simulated calorimeter. Performance is evaluated in terms of particle reconstruction quality, properties regression, and jet-level metrics. The results demonstrate that such a high-dimensional end-to-end approach succeeds in surpassing basic parametric approaches in disentangling individual neutral particles inside of jets and optimizing the use of complementary detector information. In particular, the performance comparison favors a novel architecture based on learning hypergraph structure, HGPflow, which benefits from a physically-interpretable approach to particle reconstruction.