Graph Neural Networks have attracted increasing attention in recent years. However, existing GNN frameworks are deployed based upon simple graphs, which limits their applications in dealing with complex data correlation of multi-modal/multi-type data in practice. A few hypergraph-based methods have recently been proposed to address the problem of multi-modal/multi-type data correlation by directly concatenating the hypergraphs constructed from each single individual modality/type, which is difficult to learn an adaptive weight for each modality/type. In this paper, we extend the original conference version HGNN, and introduce a general high-order multi-modal/multi-type data correlation modeling framework called HGNN$^+$ to learn an optimal representation in a single hypergraph based framework. It is achieved by bridging multi-modal/multi-type data and hyperedge with hyperedge groups. Specifically, in our method, hyperedge groups are first constructed to represent latent high-order correlations in each specific modality/type with explicit or implicit graph structures. An adaptive hyperedge group fusion strategy is then used to effectively fuse the correlations from different modalities/types in a unified hypergraph. After that a new hypergraph convolution scheme performed in spatial domain is used to learn a general data representation for various tasks. We have evaluated this framework on several popular datasets and compared it with recent state-of-the-art methods. The comprehensive evaluations indicate that the proposed HGNN$^+$ framework can consistently outperform existing methods with a significant margin, especially when modeling implicit data correlations. We also release a toolbox called THU-DeepHypergraph for the proposed framework, which can be used for various of applications, such as data classification, retrieval and recommendation.

We introduce Hyper-YOLO, a new object detection method that integrates hypergraph computations to capture the complex high-order correlations among visual features. Traditional YOLO models, while powerful, have limitations in their neck designs that restrict the integration of cross-level features and the exploitation of high-order feature interrelationships. To address these challenges, we propose the Hypergraph Computation Empowered Semantic Collecting and Scattering (HGC-SCS) framework, which transposes visual feature maps into a semantic space and constructs a hypergraph for high-order message propagation. This enables the model to acquire both semantic and structural information, advancing beyond conventional feature-focused learning. Hyper-YOLO incorporates the proposed Mixed Aggregation Network (MANet) in its backbone for enhanced feature extraction and introduces the Hypergraph-Based Cross-Level and Cross-Position Representation Network (HyperC2Net) in its neck. HyperC2Net operates across five scales and breaks free from traditional grid structures, allowing for sophisticated high-order interactions across levels and positions. This synergy of components positions Hyper-YOLO as a state-of-the-art architecture in various scale models, as evidenced by its superior performance on the COCO dataset. Specifically, Hyper-YOLO-N significantly outperforms the advanced YOLOv8-N and YOLOv9-T with 12% $\rm{AP}^{val}$ and 9% $\rm{AP}^{val}$ improvements. The source codes are at https://github.com/iMoonLab/Hyper-YOLO .

Patient survival prediction based on gigapixel whole-slide histopathological images (WSIs) has become increasingly prevalent in recent years. A key challenge of this task is achieving an informative survival-specific global representation from those WSIs with highly complicated data correlation. This paper proposes a multi-hypergraph based learning framework, called “HGSurvNet,” to tackle this challenge. HGSurvNet achieves an effective high-order global representation of WSIs via multilateral correlation modeling in multiple spaces and a general hypergraph convolution network. It has the ability to alleviate over-fitting issues caused by the lack of training data by using a new convolution structure called hypergraph max-mask convolution. Extensive validation experiments were conducted on three widely-used carcinoma datasets: Lung Squamous Cell Carcinoma (LUSC), Glioblastoma Multiforme (GBM), and National Lung Screening Trial (NLST). Quantitative analysis demonstrated that the proposed method consistently outperforms state-of-the-art methods, coupled with the Bayesian Concordance Readjust loss. We also demonstrate the individual effectiveness of each module of the proposed framework and its application potential for pathology diagnosis and reporting empowered by its interpretability potential.

The goal of the hypergraph foundation model (HGFM) is to learn an encoder based on the hypergraph computational paradigm through self-supervised pretraining on high-order correlation structures, enabling the encoder to rapidly adapt to various downstream tasks in scenarios, where no labeled data or only a small amount of labeled data are available. The initial exploratory work has been applied to brain disease diagnosis tasks. However, existing methods primarily rely on graph-based approaches to learn low-order correlation patterns between brain regions in brain networks, neglecting the modeling and learning of complex correlations between different brain diseases and patients. This article proposes an HGFM for brain disease diagnosis, which conducts multidimensional pretraining tasks to explore latent cross-dimensional high-order correlation patterns on various brain disease datasets. HGFM is a high-order correlation-driven foundation model for brain disease diagnosis and effectively improves prediction performance. Specifically, HGFM first performs brain functional network link prediction tasks on individual brain networks and group interaction network link prediction tasks on group brain networks, constructing an HGFM for brain disease diagnosis. In downstream tasks, it achieves predictions for different brain disease diagnosis tasks through few-shot learning fine-tuning methods. The proposed method is evaluated on functional magnetic resonance imaging (fMRI) data from 4409 patients across four brain diseases. Results show that it outperforms existing state-of-the-art methods in all brain disease diagnosis tasks, demonstrating its potential value in clinical applications.

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.

The isomorphism problem is a fundamental problem in network analysis, which involves capturing both low-order and high-order structural information. In terms of extracting low-order structural information, graph isomorphism algorithms analyze the structural equivalence to reduce the solver space dimension, which demonstrates its power in many applications, such as protein design, chemical pathways, and community detection. For the more commonly occurring high-order relationships in real-life scenarios, the problem of hypergraph isomorphism, which effectively captures these high-order structural relationships, cannot be straightforwardly addressed using graph isomorphism methods. Besides, the existing hypergraph kernel methods may suffer from high memory consumption or inaccurate sub-structure identification, thus yielding sub-optimal performance. In this paper, to address the abovementioned problems, we first propose the hypergraph Weisfiler-Lehman test algorithm for the hypergraph isomorphism test problem by generalizing the Weisfiler-Lehman test algorithm from graphs to hypergraphs. Secondly, based on the presented algorithm, we propose a general hypergraph Weisfieler-Lehman kernel framework and implement two instances, which are Hypergraph Weisfeiler-Lehamn Subtree Kernel (Hypergraph WL Subtree Kernel) and Hypergraph Weisfeiler-Lehamn Hyperedge Kernel (Hypergraph WL Hyperedge Kernel). The Hypergraph WL Subtree Kernel counts different types of rooted subtrees and generates the final feature vector for a given hypergraph by comparing the number of different types of rooted subtrees. The Hypergraph WL Hyperedge Kernel is developed to process hypergraphs with more degrees of hyperedges, which counts the vertex labels that are connected by each hyperedge to generate the feature vector. Mathematically, we prove the proposed Hypergraph WL Subtree Kernel can degenerate into the typical Graph Weisfeiler-Lehman Subtree Kernel when dealing with low-order graph structures. In order to fulfill our research objectives, a comprehensive set of experiments was meticulously designed, including seven graph classification datasets and 12 hypergraph classification datasets. Results on graph classification datasets indicate that the Hypergraph WL Subtree Kernel can achieve the same performance compared with the classical Graph Weisfeiler-Lehman Subtree Kernel. Results on hypergraph classification datasets show significant improvements compared to other typical kernel-based methods, which demonstrates the effectiveness of the proposed methods. In our evaluation, we found that our proposed methods outperform the second-best method in terms of runtime, running over 80 times faster when handling complex hypergraph structures. This significant speed advantage highlights the great potential of our methods in real-world applications.