Retrieval-Augmented Generation (RAG) enhances the response quality and domain-specific performance of large language models (LLMs) by incorporating external knowledge to combat hallucinations. In recent research, graph structures have been integrated into RAG to enhance the capture of semantic relations between entities. However, it primarily focuses on low-order pairwise entity relations, limiting the high-order associations among multiple entities. Hypergraph-enhanced approaches address this limitation by modeling multi-entity interactions via hyperedges, but they are typically constrained to inter-chunk entity-level representations, overlooking the global thematic organization and alignment across chunks. Drawing inspiration from the top-down cognitive process of human reasoning, we propose a theme-aligned dual-hypergraph RAG framework (Cog-RAG) that uses a theme hypergraph to capture inter-chunk thematic structure and an entity hypergraph to model high-order semantic relations. Furthermore, we design a cognitive-inspired two-stage retrieval strategy that first activates query-relevant thematic content from the theme hypergraph, and then guides fine-grained recall and diffusion in the entity hypergraph, achieving semantic alignment and consistent generation from global themes to local details. Our extensive experiments demonstrate that Cog-RAG significantly outperforms existing state-of-the-art baseline approaches.

Hypergraph Neural Networks (HGNNs) enhance graph-based modeling by representing complex relationships, with applications in brain network analysis, recommendation systems, and computer vision. However, conventional HGNNs often struggle with effective knowledge extraction and discriminative feature representation, leading to performance limitations. This paper presents Knowledge-Embedded Hypergraph Neural Networks (Knowledge HGNN), a framework that addresses these challenges with two complementary encoders and a multi-dimensional fusion strategy. The High-Order Incidence Encoder (HOI-Encoder) explicitly embeds structural knowledge by capturing permutation-invariant high-order incidence patterns that are typically overlooked by standard HGNNs. In contrast, the Task-Driven Rule Encoder (TDR-Encoder) focuses on feature-level knowledge, extracting task-related rules from vertex attributes through gradient boosted decision tree pre-training and encoding both rule content and positional importance. A Multi-Dimensional Knowledge Fusion module then integrates structural and rule-based embeddings, bridging semantic and dimensional gaps to form enriched vertex representations. The framework includes two implementations: Rule-Driven HGNN, which emphasizes rule-based knowledge, and Dual-Driven HGNN, which jointly leverages structural and rule-based knowledge for comprehensive feature extraction. Extensive experiments on ten datasets, together with ablation studies, demonstrate that Knowledge HGNN significantly improves performance, achieving a 7.3% gain on the Cora dataset and an average improvement of 2.5% across all datasets. These results highlight the effectiveness of explicitly differentiating and fusing structural and rule-based knowledge, setting a new standard for hypergraph applications in complex, data-driven scenarios.

Hypergraph Neural Networks (HGNNs) are crucial in modeling complex high-order correlations in diverse domains, utilizing hyperedges that connect multiple vertices. However, their susceptibility to structural attacks and irrational connections can disrupt message propagation and degrade performance. To address these issues, we introduce the HGNN Shield, a defense framework incorporating two key modules: Hyperedge-Dependent Estimation (HDE) and High-Order Shield (HOS). The HDE module prioritizes vertex dependencies within hyperedges and adapts traditional connectivity measures to hypergraphs, facilitating precise structural modifications. This adaptation allows for a nuanced assessment of vertex relationships within hyperedges, contributing theoretically by extending classical graph-based connection dependency measures to hypergraphs. Following HDE, the HOS module, positioned before convolutional layers, consists of three submodules: Hyperpath Cut, Hyperpath Link, and Hyperpath Refine. These components collectively detect, disconnect, and refine adversarial connections, ensuring robust message propagation. The theoretical contribution of the HOS module lies in maintaining hyperpath integrity and learning trajectory under adversarial conditions, providing a certifiable defense mechanism against high-order structural attacks. Experiments on six hypergraph datasets indicate that HGNN Shield significantly enhances robustness and maintains data integrity against targeted attacks, outperforming existing methods (an average performance improvement of 9.33% over other methods). Our framework not only improves HGNN reliability but also advances security in hypergraph-based applications.

Hypergraph neural networks (HGNNs) effectively model complex high-order relationships in domains like protein interactions and social networks by connecting multiple vertices through hyperedges, enhancing modeling capabilities, and reducing information loss. Developing foundation models for hypergraphs is challenging due to their distinct data, which includes both vertex features and intricate structural information. We present Hyper-FM, a Hypergraph Foundation Model for multi-domain knowledge extraction, featuring Hierarchical High-Order Neighbor Guided Vertex Knowledge Embedding for vertex feature representation and Hierarchical Multi-Hypergraph Guided Structural Knowledge Extraction for structural information. Additionally, we curate 11 text-attributed hypergraph datasets to advance research between HGNNs and LLMs. Experiments on these datasets show that Hyper-FM outperforms baseline methods by approximately 13.4%, validating our approach. Furthermore, we propose the first scaling law for hypergraph foundation models, demonstrating that increasing domain diversity significantly enhances performance, unlike merely augmenting vertex and hyperedge counts. This underscores the critical role of domain diversity in scaling hypergraph models.

Hypergraph neural networks (HGNNs) are widely used models for analyzing higher-order relational data. HGNNs suffer from the rapid performance degradation with increasing layers. Hypergraph dynamic system (HDS) is a potential way to deal with this challenge. However, hypergraph dynamic system is confined to a time-continuous isotropic model, lacking positional information in the structural space of the hypergraph. In contrast, anisotropic diffusion can capture structural space differences among vertices, providing a more precise representation of the information propagation process in hypergraph structures than isotropic diffusion. In this paper, we introduce HGNNv2, a stable hypergraph neural network, which is built as a hypergraph dynamic system with partial differential equation (PDE). This model incorporates a position-aware anisotropic diffusion term and an external control term. We further present the vertex-rooted subtree method to determine anisotropic diffusion intensity. HGNNv2 has properties that vertices occupying equivalent positions in the structural space share equivalent structural labels and positional features. Experiments on 6 hypergraph datasets and 3 graph datasets reveal that HGNNv2 outperforms all 12 compared methods. HGNNv2 is capable of achieving stable final representations and task accuracy even under noisy conditions. HGNNv2 achieves stable performance with fewer layers than hypergraph dynamic systems employing isotropic diffusion. We provide feature visualizations to illustrate the evolution of representations.

Designing expressive hypergraph kernels that can effectively capture high-order structural information is a fundamental challenge in hypergraph learning. In this paper, we propose a novel comparison framework based on hypergraph homomorphisms to evaluate and compare the expressive ability of existing hypergraph kernels. We revisit classical kernels such as Hypergraph Weisfeiler-Lehman (HG WL) and Hypergraph Rooted kernels, providing theoretical conditions under which they fail to distinguish non-isomorphic hypergraphs. Motivated by these insights, we introduce the Hypergraph Subtree-Cycle Kernel, which augments subtree-based features with cycle-based structural patterns to enhance expressiveness. We propose two variants: HG SCKernelv1 and HG SCKernelv2. Extensive experiments on five graph and ten hypergraph classification benchmarks demonstrate the superior performance of our methods, confirming the effectiveness of integrating homomorphism-guided design into hypergraph kernels.

Existing benchmarks like NLGraph and GraphQA evaluate LLMs on graphs by focusing mainly on pairwise relationships, overlooking the high-order correlations found in real-world data. Hypergraphs, which can model complex beyond-pairwise relationships, offer a more robust framework but are still underexplored in the context of LLMs. To address this gap, we introduce LLM4Hypergraph, the first comprehensive benchmark comprising 21,500 problems across eight low-order, five high-order, and two isomorphism tasks, utilizing both synthetic and real-world hypergraphs from citation networks and protein structures. We evaluate six prominent LLMs, including GPT-4o, demonstrating our benchmark’s effectiveness in identifying model strengths and weaknesses. Our specialized prompt- ing framework incorporates seven hypergraph languages and introduces two novel techniques, Hyper-BAG and Hyper-COT, which enhance high-order reasoning and achieve an average 4% (up to 9%) performance improvement on structure classification tasks. This work establishes a foundational testbed for integrating hypergraph computational capabilities into LLMs, advancing their comprehension.

Cross-modal 3D shape retrieval is a crucial and widely applied task in the field of 3D vision. Its goal is to construct retrieval representations capable of measuring the similarity between instances of different 3D modalities. However, existing methods face challenges due to the performance bottlenecks of single-modal representation extractors and the modality gap across 3D modalities. To tackle these issues, we propose a Heterogeneous Dynamic Graph Representation (HDGR) network, which incorporates context-dependent dynamic relations within a heterogeneous framework. By capturing correlations among diverse 3D objects, HDGR overcomes the limitations of ambiguous representations obtained solely from instances. Within the context of varying mini-batches, dynamic graphs are constructed to capture proximal intra-modal relations, and dynamic bipartite graphs represent implicit cross-modal relations, effectively addressing the two challenges above. Subsequently, message passing and aggregation are performed using Dynamic Graph Convolution (DGConv) and Dynamic Bipartite Graph Convolution (DBConv), enhancing features through heterogeneous dynamic relation learning. Finally, intra-modal, cross-modal, and self-transformed features are redistributed and integrated into a heterogeneous dynamic representation for cross-modal 3D shape retrieval. HDGR establishes a stable, context-enhanced, structure-aware 3D shape representation by capturing heterogeneous inter-object relationships and adapting to varying contextual dynamics. Extensive experiments conducted on the ModelNet10, ModelNet40, and real-world ABO datasets demonstrate the state-of-the-art performance of HDGR in cross-modal and intra-modal retrieval tasks. Moreover, under the supervision of robust loss functions, HDGR achieves remarkable cross-modal retrieval against label noise on the 3D MNIST dataset. The comprehensive experimental results highlight the effectiveness and efficiency of HDGR on cross-modal 3D shape retrieval.

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% and 9% improvements.

Hypergraphs, with their ability to model complex, beyond pair-wise correlations, presents a significant advancement over traditional graphs for capturing intricate relational data across diverse domains. However, the integration of hypergraphs into self-supervised learning (SSL) frameworks has been hindered by the intricate nature of high-order structural variations. This paper introduces the Self-Supervised Hypergraph Training Framework via Structure-Aware Learning (SS-HT), designed to enhance the perception and measurement of these variations within hypergraphs. The SS-HT framework employs a "Masking and Re-Masking" strategy to bolster feature reconstruction in Hypergraph Neural Networks (HGNNs), addressing the limitations of traditional SSL methods. It also introduces a metric strategy for local high-order correlation changes, streamlining the computational efficiency of structural distance calculations. Extensive experiments on 11 datasets demonstrate SS-HT's superior performance over existing SSL methods for both low-order and high-order data. Notably, the framework significantly reduces data labeling dependency, achieving a 32% improvement over HGNN in the downstream task fine-tuning phase under the 1% labeled data setting in the Cora-CC dataset. Ablation studies further validate SS-HT's scalability and its capacity to augment the performance of various HGNN methods, underscoring its robustness and applicability in real-world scenarios.

Hypergraph Neural Networks (HGNNs) have attracted much attention for high-order structural data learning. Existing methods mainly focus on simple mean-based aggregation or manually combining multiple aggregations to capture multiple information on hypergraphs. However, those methods inherently lack continuous non-linear modeling ability and are sensitive to varied distributions. Although some kernel-based aggregations on GNNs and CNNs can capture non-linear patterns to some degree, those methods are restricted in the low-order correlation and may cause unstable computation in training. In this work, we introduce Kernelized Hypergraph Neural Networks (KHGNN) and its variant, Half-Kernelized Hypergraph Neural Networks (H-KHGNN), which synergize mean-based and max-based aggregation functions to enhance representation learning on hypergraphs. KHGNN's kernelized aggregation strategy adaptively captures both semantic and structural information via learnable parameters, offering a mathematically grounded blend of kernelized aggregation approaches for comprehensive feature extraction. H-KHGNN addresses the challenge of overfitting in less intricate hypergraphs by employing non-linear aggregation selectively in the vertex-to-hyperedge message-passing process, thus reducing model complexity. Our theoretical contributions reveal a bounded gradient for kernelized aggregation, ensuring stability during training and inference. Empirical results demonstrate that KHGNN and H-KHGNN outperform state-of-the-art models across 10 graph/hypergraph datasets, with ablation studies demonstrating the effectiveness and computational stability of our method.

Existing cross-domain image retrieval (CDIR) methods exhibit a strong dependency on prior knowledge of training categories, which leads to problems of class confusion and domain shift when encountering unseen categories in open-set environments. In this paper, we explore the CDIR task towards open-set environments and introduce the Hypergraph-Based Remaining Prototype Alignment (RePro) framework for this task. Specifically, to address the problem of unseen class confusion caused by the category differences, we utilize the Remaining Prototype Embedding (RPE) module to generate the remaining embeddings of images and treat these embeddings as domain noise, rather than directly mapping them to the explicit domain-unified prototypes. To overcome the problem of domain shift, our method leverages the high-order correlations among both domains and categories through the Heterogeneous Structure Alignment (HSA) module, by constructing a heterogeneous hypergraph based on intra-domain and inter-category correlations. Besides, we build two multi-domain datasets for open-set cross-domain image retrieval,i.e., OCD-PACS and OCD-VLCS. Each dataset is divided into seen and unseen categories for training and testing, and each class has four different domains of images. Extensive experiments and ablation studies on these two datasets demonstrate the superiority of our method over current state-of-the-art methods.

Existing 3D cross-modal retrieval (3CMR) methods heavily rely on prior knowledge of training categories, which leads to the problem of modality shift and unseen center deviation when encountering unseen categories under the open-set environment. Aiming at the open-set 3CMR, this paper introduces the Hypergraph-Based Residual Fuzzy Alignment (ReFA) framework, which revisits the open-set retrieval task and navigates uncertainty of it through the lens ofFuzzy Theory. Facing the challenges of boundaryless space caused by uncertain unseen categories, we explore the representation and measurement in the fuzzy membership space as an alternative to fixed close-set category space. Specifically, to address the problem of modality shift caused by unseen categories, we utilize the Residual Sampling Generation (RSG) module to generate modality sampling embeddings that are independent of seen categories under the guidance of fuzzy representation, which residually decouples the entangled interactions of seen categories and modalities. To overcome the problem of unseen center deviation, we propose the Center Fuzzy Alignment (CFA) module to leverage the high-order fuzzy correlations for generalized metric, by constructing a fuzzy hypergraph based on the inherent and fuzzy correlations among both modalities and categories. The comprehensive evaluations of comparison and ablation studies on the four benchmarks demonstrate the superiority of our proposed framework compared to state-of-the-art methods.

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.

The hypergraph neural network (HGNN) is an emerging powerful tool for modeling and learning complex, high-order correlations among entities upon hypergraph structures. While existing HGNN-based approaches excel in modeling high-order correlations among data using hyperedges, they often have difficulties in distinguishing diverse semantics (e.g., bioactivities between drug and target in biological networks) of different correlations, making it challenging to learn accurate final representations. The underlying reason is that the specific semantic information of each hyperedge cannot be captured and distinguished during the modeling and learning process. To address this, we propose a mode HGNN ( $\textsf {MHGNN}$ ) framework that extends the vanilla hypergraph structure by endowing hyperedges with mode information for encapsulating their semantics and then performs mode-aware high-order message passing upon mode hypergraph for achieving comprehensive node representations. Extensive evaluations on four real-world datasets under two representative tasks have demonstrated the outstanding performance of $\textsf {MHGNN}$ against the state of the arts.

Three-dimensional in-domain retrieval has recently achieved significant success, but 3-D cross-modal retrieval still faces problems and challenges. Existing methods only rely on a simple global feature (GF), which overlooks the local information of complex 3-D objects and the connections between similar local features across complex multimodal instances. To tackle this issue, we propose a hierarchical set-to-set representation (HSR) and a corresponding hierarchical similarity that incorporates global-to-global and local-to-local similarity metrics. Specifically, we employ feature extractors for each modality to learn both GFs and local feature sets. We then project these features into their respective common space and use bilinear pooling to generate compact-set features that maintain the invariant for set-to-set similarity measurement. To facilitate effective hierarchical similarity measurement, we design an operation to combine the GF and the compact-set feature to generate the hierarchical representation for 3-D cross-modal retrieval, which preserves hierarchical similarity measurement. To optimize the framework, we adopt the joint loss functions, including cross-modal center loss (CMCL), mean square loss, and cross-entropy loss, to reduce the cross-modal discrepancy for each instance and minimize the distances between the instances in the same category. Experimental results demonstrate that our method outperforms the state-of-the-art methods on the 3-D cross-modal retrieval task on both ModelNet10 and ModelNet40 datasets.

Hypergraph Neural Networks (HGNNs) have recently attracted much attention and exhibited satisfactory performance due to their superiority in high-order correlation modeling. However, it is noticed that the high-order modeling capability of hypergraph also brings increased computation complexity, which hinders its practical industrial deployment. In practice, we find that one key barrier to the efficient deployment of HGNNs is the high-order structural dependencies during inference. In this paper, we propose to bridge the gap between the HGNNs and inference-efficient Multi-Layer Perceptron (MLPs) to eliminate the hypergraph dependency of HGNNs and thus reduce computational complexity as well as improve inference speed. Specifically, we introduce LightHGNN and LightHGNN$^+$ for fast inference with low complexity. LightHGNN directly distills the knowledge from teacher HGNNs to student MLPs via soft labels, and LightHGNN$^+$ further explicitly injects reliable high-order correlations into the student MLPs to achieve topology-aware distillation and resistance to over-smoothing. Experiments on eight hypergraph datasets demonstrate that even without hypergraph dependency, the proposed LightHGNNs can still achieve competitive or even better performance than HGNNs and outperform vanilla MLPs by $16.3$ on average. Extensive experiments on three graph datasets further show the average best performance of our LightHGNNs compared with all other methods. Experiments on synthetic hypergraphs with 5.5w vertices indicate LightHGNNs can run $100\times$ faster than HGNNs, showcasing their ability for latency-sensitive deployments.

Recently, hypergraph neural networks (HGNNs) exhibit the potential to tackle tasks with high-order correlations and have achieved success in many tasks. However, existing evolution on the hypergraph has poor controllability and lacks sufficient theoretical support (like dynamic systems), thus yielding sub-optimal performance. One typical scenario is that only one or two layers of HGNNs can achieve good results and more layers lead to degeneration of performance. Under such circumstances, it is important to increase the controllability of HGNNs. In this paper, we first introduce hypergraph dynamic systems (HDS), which bridge hypergraphs and dynamic systems and characterize the continuous dynamics of representations. We then propose a control-diffusion hypergraph dynamic system by an ordinary differential equation (ODE). We design a multi-layer HDS$^{ode}$ as a neural implementation, which contains control steps and diffusion steps. HDS$^{ode}$ has the properties of controllability and stabilization and is allowed to capture long-range correlations among vertices. Experiments on $9$ datasets demonstrate HDS$^{ode}$ beat all compared methods. HDS$^{ode}$ achieves stable performance with increased layers and solves the poor controllability of HGNNs. We also provide the feature visualization of the evolutionary process to demonstrate the controllability and stabilization of HDS$^{ode}$.

Existing methods of 3D cross-modal retrieval heavily lean on category distribution priors within the training set, which diminishes their efficacy when tasked with unseen categories under open-set environments. To tackle this problem, we propose the Structure-Aware Residual-Center Representation (SRCR) framework for self-supervised open-set 3D cross-modal retrieval. To address the center deviation due to category distribution differences, we utilize the Residual-Center Embedding (RCE) for each object by nested auto-encoders, rather than directly mapping them to the modality or category centers. Besides, we perform the Hierarchical Structure Learning (HSL) approach to leverage the high-order correlations among objects for generalization, by constructing a heterogeneous hypergraph structure based on hierarchical inter-modality, intra-object, and implicit-category correlations. Extensive experiments and ablation studies on four benchmarks demonstrate the superiority of our proposed framework compared to state-of-the-art methods.

In open-set environments, the introduction of unseen classes adds a third stage of data for incremental learning, alongside seen classes of old and new. Existing methods by binary optimization between old and new classes struggle to model the complex triadic relationships among old, new, and unseen classes. In this paper, we introduce the Triadic Elastic Structure Learning (TESR) framework for open-set incremental 3D object retrieval. Specifically, to overcome the Bi-Directional Catastrophic Forgetting (BDCF) problem in open-set incremental learning, we employ the Triadic Regularized Embedding (TRE) module. This module helps to globally preserve the triadic relationships among the three stages of classes, while simultaneously facilitating semantic-specific learning for new classes from a local perspective. To address the challenge of Bi-Directional Knowledge Transfer (BDKT), our method leverages high-order correlations among objects of different classes through the Elastic Structure Distillation (ESD) module, by constructing an elastic hypergraph based on incremental and global correlations. We construct four multi-modal datasets for this open-set incremental 3D object retrieval: OIES, OINT, OIMN, and OIAB. Extensive experiments and ablation studies on these four benchmarks demonstrate the superiority of our method over current state-of-the-art approaches.

We study the problem of retrieving accurate correspondence through multi-scale consistency (MSC) for robust point cloud registration. Existing works in a coarse-to-fine manner either suffer from severe noisy correspondences caused by unreliable coarse matching or struggle to form outlier-free coarse-level correspondence sets. To tackle this, we present Hierarchical Sinkhorn Tree (HST), a pruned tree structure designed to hierarchically measure the local consistency of each coarse correspondence across multiple feature scales, thereby filtering out the local dissimilar ones. In this way, we convert the modeling of MSC for each correspondence into a BFS traversal with pruning of a K-ary tree rooted at the superpoint, with its K nearest neighbors in the feature pyramid serving as child nodes. To achieve efficient pruning and accurate vicinity characterization, we further propose a novel overlap-aware Sinkhorn Distance, which retains only the most likely overlapping points for local measurement and next level exploration. The modeling process essentially involves traversing a pair of HSTs synchronously and aggregating the consistency measures of corresponding tree nodes. Extensive experiments demonstrate HST consistently outperforms the state-of-the-art methods on both indoor and outdoor benchmarks.

Existing open-set learning methods consider only the single-layer labels of objects and strictly assume no overlap between the training and testing sets, leading to contradictory optimization for superposed categories. In this paper, we introduce a more practical Semi-Open Environment setting for open-set 3D object retrieval with hierarchical labels, in which the training and testing set share a partial label space for coarse categories but are completely disjoint from fine categories. We propose the Hypergraph-Based Hierarchical Equilibrium Representation (HERT) framework for this task. Specifically, we propose the Hierarchical Retrace Embedding (HRE) module to overcome the global disequilibrium of unseen categories by fully leveraging the multi-level category information. Besides, tackling the feature overlap and class confusion problem, we perform the Structured Equilibrium Tuning (SET) module to utilize more equilibrial correlations among objects and generalize to unseen categories, by constructing a superposed hypergraph based on the local coherent and global entangled correlations. Furthermore, we generate four semi-open 3DOR datasets with multi-level labels for benchmarking. Results demonstrate that the proposed method can effectively generate the hierarchical embeddings of 3D objects and generalize them towards semi-open environments.

The lack of object-level labels presents a significant challenge for 3D object retrieval in the open-set environment. However, part-level shapes of objects often share commonalities across categories but remain underexploited in existing retrieval methods. In this paper, we introduce the Hypergraph-Based Assembly Fuzzy Representation (HARF) framework, which navigates the intricacies of open-set 3D object retrieval through a bottom-up lens of Part Assembly. To tackle the challenge of assembly isomorphism and unification, we propose the Hypergraph Isomorphism Convolution (HIConv) for smoothing and adopt the Isomorphic Assembly Embedding (IAE) module to generate assembly embeddings with geometric-semantic consistency. To address the challenge of open-set category generalization, our method employs high-order correlations and fuzzy representation to mitigate distribution skew through the Structure Fuzzy Reconstruction (SFR) module, by constructing a leveraged hypergraph based on local certainty and global uncertainty correlations. We construct three open-set retrieval datasets for 3D objects with part-level annotations: OP-SHNP, OP-INTRA, and OP-COSEG. Extensive experiments and ablation studies on these three benchmarks show our method outperforms current state-of-the-art methods.

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.

The traditional 3D object retrieval (3DOR) task is under the close-set setting, which assumes the categories of objects in the retrieval stage are all seen in the training stage. Existing methods under this setting may tend to only lazily discriminate their categories, while not learning a generalized 3D object embedding. Under such circumstances, it is still a challenging and open problem in real-world applications due to the existence of various unseen categories. In this paper, we first introduce the open-set 3DOR task to expand the applications of the traditional 3DOR task. Then, we propose the Hypergraph-Based Multi-Modal Representation (HGM$^{2}$R) framework to learn 3D object embeddings from multi-modal representations under the open-set setting. The proposed framework is composed of two modules, i.e., the Multi-Modal 3D Object Embedding (MM3DOE) module and the Structure-Aware and Invariant Knowledge Learning (SAIKL) module. By utilizing the collaborative information of modalities derived from the same 3D object, the MM3DOE module is able to overcome the distinction across different modality representations and generate unified 3D object embeddings. Then, the SAIKL module utilizes the constructed hypergraph structure to model the high-order correlation among 3D objects from both seen and unseen categories. The SAIKL module also includes a memory bank that stores typical representations of 3D objects. By aligning with those memory anchors in the memory bank, the aligned embeddings can integrate the invariant knowledge to exhibit a powerful generalized capacity toward unseen categories. We formally prove that hypergraph modeling has better representative capability on data correlation than graph modeling. We generate four multi-modal datasets for the open-set 3DOR task, i.e., OS-ESB-core, OS-NTU-core, OS-MN40-core, and OS-ABO-core, in which each 3D object contains three modality representations: multi-view, point clouds, and voxel. Experiments on these four datasets show that the proposed method can significantly outperform existing methods. In particular, the proposed method outperforms the state-of-the-art by 12.12%/12.88% in terms of mAP on the OS-MN40-core/OS-ABO-core dataset, respectively. Results and visualizations demonstrate that the proposed method can effectively extract the generalized 3D object embeddings on the open-set 3DOR task and achieve satisfactory performance.

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.

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 article 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.

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.

Collaborative filtering (CF) is one of the most popular and important recommendation methodologies in the heart of numerous recommender systems today. Although widely adopted, existing CF-based methods, ranging from matrix factorization to the emerging graph-based methods, suffer inferior performance especially when the data for training are very limited. In this paper, we first pinpoint the root causes of such deficiency and observe two main disadvantages that stem from the inherent designs of existing CF-based methods, i.e., 1) inflexible modeling of users and items and 2) insufficient modeling of high-order correlations among the subjects. Under such circumstances, we propose a dual channel hypergraph collaborative filtering (DHCF) framework to tackle the above issues. First, a dual channel learning strategy, which holistically leverages the divide-and-conquer strategy, is introduced to learn the representation of users and items so that these two types of data can be elegantly interconnected while still maintaining their specific properties. Second, the hypergraph structure is employed for modeling users and items with explicit hybrid high-order correlations. The jump hypergraph convolution (JHConv) method is proposed to support the explicit and efficient embedding propagation of high-order correlations. Comprehensive experiments on two public benchmarks and two new real-world datasets demonstrate that DHCF can achieve significant and consistent improvements against other state-of-the-art methods.

Mesh is an important and powerful type of data for 3D shapes and widely studied in the field of computer vision and computer graphics. Regarding the task of 3D shape representation, there have been extensive research efforts concentrating on how to represent 3D shapes well using volumetric grid, multi-view and point cloud. However, there is little effort on using mesh data in recent years, due to the complexity and irregularity of mesh data. In this paper, we propose a mesh neural network, named MeshNet, to learn 3D shape representation from mesh data. In this method, face-unit and feature splitting are introduced, and a general architecture with available and effective blocks are proposed. In this way, MeshNet is able to solve the complexity and irregularity problem of mesh and conduct 3D shape representation well. We have applied the proposed MeshNet method in the applications of 3D shape classification and retrieval. Experimental results and comparisons with the state-of-the-art methods demonstrate that the proposed MeshNet can achieve satisfying 3D shape classification and retrieval performance, which indicates the effectiveness of the proposed method on 3D shape representation.

In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for complex data in real practice, we propose to incorporate such data structure in a hypergraph, which is more flexible on data modeling, especially when dealing with complex data. In this method, a hyperedge convolution operation is designed to handle the data correlation during representation learning. In this way, traditional hypergraph learning procedure can be conducted using hyperedge convolution operations efficiently. HGNN is able to learn the hidden layer representation considering the high-order data structure, which is a general framework considering the complex data correlations. We have conducted experiments on citation network classification and visual object recognition tasks and compared HGNN with graph convolutional networks and other traditional methods. Experimental results demonstrate that the proposed HGNN method outperforms recent state-of-theart methods. We can also reveal from the results that the proposed HGNN is superior when dealing with multi-modal data compared with existing methods.

Three-dimensional (3D) shape recognition has drawn much research attention in the field of computer vision. The advances of deep learning encourage various deep models for 3D feature representation. For point cloud and multi-view data, two popular 3D data modalities, different models are proposed with remarkable performance. However the relation between point cloud and views has been rarely investigated. In this paper, we introduce Point-View Relation Network (PVRNet), an effective network designed to well fuse the view features and the point cloud feature with a proposed relation score module. More specifically, based on the relation score module, the point-single-view fusion feature is first extracted by fusing the point cloud feature and each single view feature with point-singe-view relation, then the pointmulti- view fusion feature is extracted by fusing the point cloud feature and the features of different number of views with point-multi-view relation. Finally, the point-single-view fusion feature and point-multi-view fusion feature are further combined together to achieve a unified representation for a 3D shape. Our proposed PVRNet has been evaluated on ModelNet40 dataset for 3D shape classification and retrieval. Experimental results indicate our model can achieve significant performance improvement compared with the state-of-the-art models.

Over the past decade, increasing research efforts have been concentrated on emotion recognition from physiological signals due to their capability on emotion information representation. Existing works mainly focus on exploring the relationship between stimulus and subjects, while ignoring the effects of latent correlations among different subjects, which are important for personalized emotion recognition. To tackle this issue, we aim to conduct emotion recognition using multi-modal physiological signals through an edge-weighted hyper-graph neural network, in which complex relationship among subjects is formulated using hypergraph for each modality respectively. In our model, the differences in significance of influence which various samples leave on the classification can be better represented. The major contribution of this network lies in its concern that the associate strengths between various samples are different, which have different impact on the training result. The hyperedge between the vertices with closer correlation should be assigned a larger weight. Reversely, the looser relation, the minor weight. To evaluate the proposed method, experiments have been conducted on the DEAP dataset and ASCERTAIN dataset. Experimental results and comparison with state-of-the-art methods show that the proposed method can achieve better performance.

In recent years, graph/hypergraph-based deep learning methods have attracted much attention from researchers. These deep learning methods take graph/hypergraph structure as prior knowledge in the model. However, hidden and important relations are not directly represented in the inherent structure. To tackle this issue, we propose a dynamic hypergraph neural networks framework (DHGNN), which is composed of the stacked layers of two modules: dynamic hypergraph construction (DHG) and hypergrpah convolution (HGC). Considering initially constructed hypergraph is probably not a suitable representation for data, the DHG module dynamically updates hypergraph structure on each layer. Then hypergraph convolution is introduced to encode high-order data relations in a hypergraph structure. The HGC module includes two phases: vertex convolution and hyperedge convolution, which are designed to aggregate feature among vertices and hyperedges, respectively. We have evaluated our method on standard datasets, the Cora citation network and Microblog dataset. Our method outperforms state-of-the-art methods. More experiments are conducted to demonstrate the effectiveness and robustness of our method to diverse data distributions.

3D shape recognition has attracted much attention recently. Its recent advances advocate the usage of deep features and achieve the state-of-the-art performance. However, existing deep features for 3D shape recognition are restricted to a view-to-shape setting, which learns the shape descriptor from the view-level feature directly. Despite the exciting progress on view-based 3D shape description, the intrinsic hierarchical correlation and discriminability among views have not been well exploited, which is important for 3D shape representation. To tackle this issue, in this paper, we propose a group-view convolutional neural network (GVCNN) framework for hierarchical correlation modeling towards discriminative 3D shape description. The proposed GVCNN framework is composed of a hierarchical view-group-shape architecture, i.e., from the view level, the group level and the shape level, which are organized using a grouping strategy. Concretely, we first use an expanded CNN to extract a view level descriptor. Then, a grouping module is introduced to estimate the content discrimination of each view, based on which all views can be splitted into different groups according to their discriminative level. A group level description can be further generated by pooling from view descriptors. Finally, all group level descriptors are combined into the shape level descriptor according to their discriminative weights. Experimental results and comparison with state-of-the-art methods show that our proposed GVCNN method can achieve a significant performance gain on both the 3D shape classification and retrieval tasks.

3D object recognition has attracted wide research attention in the field of multimedia and computer vision. With the recent proliferation of deep learning, various deep models with different representations have achieved the state-of-the-art performance. Among them, point cloud and multi-view based 3D shape representations are promising recently, and their corresponding deep models have shown significant performance on 3D shape recognition. However, there is little effort concentrating point cloud data and multi-view data for 3D shape representation, which is, in our consideration, beneficial and compensated to each other. In this paper, we propose the Point-View Network (PVNet), the first framework integrating both the point cloud and the multi-view data towards joint 3D shape recognition. More specifically, an embedding attention fusion scheme is proposed that could employ high-level features from the multi-view data to model the intrinsic correlation and discriminability of different structure features from the point cloud data. In particular, the discriminative descriptions are quantified and leveraged as the soft attention mask to further refine the structure feature of the 3D shape. We have evaluated the proposed method on the ModelNet40 dataset for 3D shape classification and retrieval tasks. Experimental results and comparisons with state-of-the-art methods demonstrate that our framework can achieve superior performance.