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.

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.

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.

Graph-based semi-supervised learning methods have been used in a wide range of real-world applications, e.g., from social relationship mining to multimedia classification and retrieval. However, existing methods are limited along with high computational complexity or not facilitating incremental learning, which may not be powerful to deal with large-scale data, whose scale may continuously increase, in real world. This paper proposes a new method called Data Distribution Based Graph Learning (DDGL) for semi-supervised learning on large-scale data. This method can achieve a fast and effective label propagation and supports incremental learning. The key motivation is to propagate the labels along smaller-scale data distribution model parameters, rather than directly dealing with the raw data as previous methods, which accelerate the data propagation significantly. It also improves the prediction accuracy since the loss of structure information can be alleviated in this way. To enable incremental learning, we propose an adaptive graph updating strategy which can update the model when there is distribution bias between new data and the already seen data. We have conducted comprehensive experiments on multiple datasets with sample sizes increasing from seven thousand to five million. Experimental results on the classification task on large-scale data demonstrate that our proposed DDGL method improves the classification accuracy by a large margin while consuming much less time compared to state-of-the-art methods.

The Kullback-Leibler divergence (KLD), which is widely used to measure the similarity between two distributions, plays an important role in many applications. In this article, we address the KLD metric-learning task, which aims at learning the best KLD-type metric from the distributions of datasets. Concretely, first, we extend the conventional KLD by introducing a linear mapping and obtain the best KLD to well express the similarity of data distributions by optimizing such a linear mapping. It improves the expressivity of data distribution, which means it makes the distributions in the same class close and those in different classes far away. Then, the KLD metric learning is modeled by a minimization problem on the manifold of all positive-definite matrices. To deal with this optimization task, we develop an intrinsic steepest descent method, which preserves the manifold structure of the metric in the iteration. Finally, we apply the proposed method along with ten popular metric-learning approaches on the tasks of 3-D object classification and document classification. The experimental results illustrate that our proposed method outperforms all other methods.

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.