Hypergraph Generation Research Articles

Automatic Hypergraph Generation for Enhancing Recommendation With Sparse Optimization

Automatic Hypergraph Generation for Enhancing Recommendation With Sparse Optimization

A hypergraph-based hybrid graph convolutional network for intracity human activity intensity prediction and geographic relationship interpretation

Human activity intensity prediction, i.e., estimating the dynamic population distribution, is crucial to many location-based applications, particularly intelligent transportation systems and urban planning. Geographical artificial intelligence (GeoAI) is an emerging field that has contributed many new modeling approaches for spatiotemporal phenomena, especially spatiotemporal graph neural networks (ST-GNNs). However, there are two challenges to the prediction of human activity intensity. On the one hand, accurate predictions require modeling not only pairwise spatial relationships, e.g., distance and spatial flow but also complex high-order relationships, such as clusters and groups. On the other hand, it is not appropriate to incorporate prior knowledge on the spatial structure of data with subjective assumptions using graphs with predefined topologies or weights. To mitigate such challenges, a novel deep learning-based model was proposed, namely, the Hypergraph-based Hybrid Graph Convolutional Network (HyGCN). In our study, high-order relationships are modeled by hypergraph convolutions, and pairwise relationships are captured in graph convolutions. A spatial fusion layer is added to fuse the pairwise and high-order relationships. Then, adaptive graph and hypergraph generation methods are proposed to interpret edge weights and understand the learned geographic relationships in accordance with principles. After systematic experiments on large-scale mobility data, our results demonstrate that HyGCN outperforms state-of-the-art models. The learned geospatial knowledge can be disentangled and explained from the perspectives of geographic principles. This study offers new insights for not only revisiting geographic laws in GeoAI but also utilizing spatiotemporal knowledge in deep learning models.

Attention based adaptive spatial–temporal hypergraph convolutional networks for stock price trend prediction

Stock price trend prediction is an important and challenging issue, and accurate forecasting will effectively improve investment decisions and contribute to investment returns. Improving prediction accuracy by exploring stock correlations has received much attention in recent studies. However, there are still some issues that have not been fully considered, such as the impact of invalid correlations, low sensitivity to minor price fluctuations and dependence on priors expert information. To solve the above issues, we propose a novel spatial–temporal framework, which has several characteristics: (1) the noise-aware spatial–temporal attention that dynamically filters out invalid associations from traditional spatial attention and combines temporal attention to capture the spatial–temporal patterns of different stock series; (2) the adaptive stock hypergraph generation maps the intrinsic associations of stocks into a trainable dense matrix via adaptive node embedding; (3) the adaptive graph convolution extends the graph convolution operation from static graphs to adaptive hypergraphs for exploring the dynamic correlations. (4) Multiple stacked attention-based adaptive spatial–temporal Blocks form the end-to-end prediction framework, which uses time-aware cascaded convolution to extract fine-grained temporal features. Convincing experimental results on two stock datasets, studies on the performance on various simulation investments and the model interpretability confirm the advantages of our approach.

Generating real-world hypergraphs via deep generative models

Hypergraph generation has found wide applications in data analysis, social networks, and communication networks. Although various hypergraph generation methods have been proposed, many challenges remain. On the one hand, traditional hypergraph generation methods are time-consuming since they rely on computing various statistics about hypergraph distributions prior to generation. On the other hand, they store many intermediate variables in the process of hypergraph generation, thus depleting a large number of memory resources, which could lead to memory explosion. To address these issues, we present a novel deep generative model for hypergraph generation (DGMH), which consists of a node selection module and a hyperedge size decision module. In DGMH, each hyperedge is treated as an embedding in a high-dimensional space, where values along specific dimensions represent the probabilities of node inclusion in the hyperedge. The node selection module captures the distribution of hyperedge embeddings and identifies other latent hyperedge embeddings within the space. In addition, the hyperedge size decision module determines the hyperedge size based on the hyperedge embedding. We sample a certain number of nodes from the categorical distribution parameterized by the embedding and assign these nodes to the hyperedge, an essential step in hyperedge generation. Once a sufficient number of hyperedges are generated, they are connected through common nodes to form a complete hypergraph. Experimental results demonstrate the effectiveness of DGMH in capturing the structural distribution of hypergraphs in a short time while maintaining a modest memory footprint during the generation process.

Hyper-Mol: Molecular Representation Learning via Fingerprint-Based Hypergraph.

With the development of artificial intelligence (AI) in the field of drug design and discovery, learning informative representations of molecules is becoming crucial for those AI-driven tasks. In recent years, the graph neural networks (GNNs) have emerged as a preferred choice of deep learning architecture and have been successfully applied to molecular representation learning (MRL). Up-to-date MRL methods directly apply the message passing mechanism on the atom-level attributes (i.e., atoms and bonds) of molecules. However, they neglect latent yet significant hyperstructured knowledge, such as the information of pharmacophore or functional class. Hence, in this paper, we propose Hyper-Mol, a new MRL framework that applies GNNs to encode hypergraph structures of molecules via fingerprint-based features. Hyper-Mol explores the hyperstructured knowledge and the latent relationships of the fingerprint substructures from a hypergraph perspective. The molecular hypergraph generation algorithm is designed to depict the hyperstructured information with the physical and chemical characteristics of molecules. Thus, the fingerprint-level message passing process can encode both the intra-structured and inter-structured information of fingerprint substructures according to the molecular hypergraphs. We evaluate Hyper-Mol on molecular property prediction tasks, and the experimental results on real-world benchmarks show that Hyper-Mol can learn comprehensive hyperstructured knowledge of molecules and is superior to the state-of-the-art baselines.

FC–HAT: Hypergraph attention network for functional brain network classification

Recently, functional brain network analysis via graph neural networks has achieved state-of-the-art results as it can directly extract information from irregular graphs without any approximation. However, current methods remain limited in exploring the high-order structural information of brain networks. To address this issue, we propose a hypergraph attention network for functional brain network classification (FC–HAT). First, we build a dynamic hypergraph generation phase and model each brain network as a hypergraph to preserve the high-order information. The pair-wise and community-wise similarities in functional brain networks are separately captured by k nearest neighbors and k-means. Theoretical analysis shows that the constructed hypergraph exhibits superior spectral properties. Then, we design a hypergraph attention aggregation phase to further extract information in hypergraphs. This includes node and hyperedge attention layers that can separately aggregate features among nodes and hyperedges. Finally, the two phases are jointly optimized in an end-to-end manner, which can dynamically update hypergraphs and node embeddings along with the training process. Experimental results on ABIDE-I and ADHD-200 demonstrate the effectiveness of FC–HAT in cerebral disease classification. Moreover, the abnormal connectivity patterns and brain regions identified by FC–HAT are found to be more likely to become biomarkers associated with cerebral diseases.

Hypergraph and Uncertain Hypergraph Representation Learning Theory and Methods

With the advent of big data and the information age, the data magnitude of various complex networks is growing rapidly. Many real-life situations cannot be portrayed by ordinary networks, while hypergraphs have the ability to describe and characterize higher order relationships, which have attracted extensive attention from academia and industry in recent years. Firstly, this paper described the development process, the application areas, and the existing review research of hypergraphs; secondly, introduced the theory of hypergraphs briefly; then, compared the learning methods of ordinary graphs and hypergraphs from three aspects: matrix decomposition, random walk, and deep learning; next, introduced the structural optimization of hypergraphs from three perspectives: dynamic hypergraphs, hyperedge weight optimization, and multimodal hypergraph generation; after that, the applicability of three uncertain hypergraph models were analyzed based on three uncertainty theories: probability theory, fuzzy set, and rough set; finally, the future research directions of hypergraphs and uncertain hypergraphs were prospected.

Hypergraph Learning: Methods and Practices.

Hypergraph learning is a technique for conducting learning on a hypergraph structure. In recent years, hypergraph learning has attracted increasing attention due to its flexibility and capability in modeling complex data correlation. In this paper, we first systematically review existing literature regarding hypergraph generation, including distance-based, representation-based, attribute-based, and network-based approaches. Then, we introduce the existing learning methods on a hypergraph, including transductive hypergraph learning, inductive hypergraph learning, hypergraph structure updating, and multi-modal hypergraph learning. After that, we present a tensor-based dynamic hypergraph representation and learning framework that can effectively describe high-order correlation in a hypergraph. To study the effectiveness and efficiency of hypergraph generation and learning methods, we conduct comprehensive evaluations on several typical applications, including object and action recognition, Microblog sentiment prediction, and clustering. In addition, we contribute a hypergraph learning development toolkit called THU-HyperG.

Resolution based algorithms for the transversal hypergraph generation problem

We study the problem, given a hypergraph H, how to generate its transversal (or dual) hypergraph G, using tools from Boolean resolution. We show how to compute the residual dual of H given a subset E of its minimal transversals. This is the hypergraph whose minimal transversals are exactly those missing from E to become the dual of H. We give a novel algorithm for the problem based on the notion of subtransversal. Though its complexity is superpolynomial, it gives new insight to the problem of hypergraph duality. Another variant of the algorithm seems also promising to efficiently test hypergraph duality in practice.

Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets

Quantum contextuality turns out to be a necessary resource for universal quantum computation and important in the field of quantum information processing. It is therefore of interest both for theoretical considerations and for experimental implementation to find new types and instances of contextual sets and develop methods of their optimal generation. We present an arbitrary exhaustive hypergraph-based generation of the most explored contextual sets---Kochen-Specker (KS) ones---in 4, 6, 8, 16, and 32 dimensions. We consider and analyse twelve KS classes and obtain numerous properties of theirs, which we then compare with the results previously obtained in the literature. We generate several thousand times more types and instances of KS sets than previously known. All KS sets in three of the classes and in the upper part of a fourth are novel. We make use of the MMP hypergraph language, algorithms, and programs to generate KS sets strictly following their definition from the Kochen-Specker theorem. This approach proves to be particularly advantageous over the parity-proof-based ones (which prevail in the literature), since it turns out that only a very few KS sets have a parity proof (in six KS classes 0.01% and in one of them 0%). MMP hypergraph formalism enables a translation of an exponentially complex task of solving systems of nonlinearequations, describing KS vector orthogonalities, into a statistically linearly complex task of evaluating vertex states of hypergraph edges, thus exponentially speeding up the generation of KS sets and enabling us to generate billions of novel instances of them. The MMP hypergraph notation also enables us to graphically represent KS sets and to visually discern their features.

A Lower Bound for the HBC Transversal Hypergraph Generation

The computation of transversal hypergraphs in output-polynomial time is a long standing open question. An Apriori-like level-wise approach referred to as the HBC-algorithm or MTminer was published in 2007 by Hebert, Bretto, and Cremilleux [A Data Mining Formalization to Improve Hypergraph Minimal Transversal Computation, Fundamenta Informaticae, 804, 2007, 415--433] and was experimentally demonstrated to have very good performance on hypergraphs with small transversals. In this short note extending the paper by Hagen [Lower bounds for three algorithms for transversal hypergraph generation, Discrete Applied Mathematics, 1577, 2009, 1460--1469], we prove a superpolynomial lower bound for the HBC-algorithm. This lower bound also shows that the originally claimed upper bound on the HBC-algorithm's running time is wrong.

A Note on Fuzzy Relational Equations With Min-Implication Composition

The fuzzy relational equations with min-implication composition are considered, where the implication operation involved is the residuum with respect to the minimum operation. The solution set of such a system of equations, whenever nonempty, can be characterized by a minimum solution and finitely many maximal solutions. It is shown that a system of fuzzy relational equations with min-implication composition can be reformulated in polynomial time into a system of 0-1 mixed integer linear inequalities, and consequently, the structure of its solution set can be revealed in a succinct manner. Besides, it is shown that the determination of all maximal solutions is polynomially reducible to the transversal hypergraph generation problem, of which some practically well-performed algorithms are available.

Lower bounds for three algorithms for transversal hypergraph generation

The computation of all minimal transversals of a given hypergraph in output-polynomial time is a long standing open question known as Transversal Hypergraph Generation. One of the first attempts at this problem—the sequential method [Claude Berge, Hypergraphs, in: North-Holland Mathematical Library, vol. 45, North-Holland, 1989]—is not output-polynomial as was shown by Takata [Ken Takata, A worst-case analysis of the sequential method to list the minimal hitting sets of a hypergraph, SIAM Journal on Discrete Mathematics 21 (4) (2007) 936–946]. Recently, three new algorithms improving the sequential method were published and experimentally shown to perform very well in practice [James Bailey, Thomas Manoukian, Kotagiri Ramamohanarao, A fast algorithm for computing hypergraph transversals and its application in mining emerging patterns, in: Proceedings of the 3rd IEEE International Conference on Data Mining, ICDM 2003, 19–22 December 2003, Melbourne, FL, USA, IEEE Computer Society, 2003, pp. 485–488; Guozhu Dong, Jinyan Li, Mining border descriptions of emerging patterns from dataset pairs, Knowledge and Information Systems 8 (2) (2005) 178–202; Dimitris J. Kavvadias, Elias C. Stavropoulos, An efficient algorithm for the transversal hypergraph generation, Journal of Graph Algorithms and Applications 9 (2) (2005) 239–264]. Nevertheless, a theoretical worst-case analysis has been pending. We close this gap by proving lower bounds for all three algorithms. Thereby, we show that none of them are output-polynomial.

An Efficient Algorithm for the Transversal Hypergraph Generation

The Transversal Hypergraph Generation is the problem of generating, given a hypergraph, the set of its minimal transversals, i.e., the hypergraph whose hyperedges are the minimal hitting sets of the given one. The purpose of this paper is to present an efficient and practical algorithm for solving this problem. We show that the proposed algorithm operates in a way that rules out regeneration and, thus, its memory requirements are polynomially bounded to the size of the input hypergraph. Although no time bound for the algorithm is given, experimental evaluation and comparison with other approaches have shown that it behaves well in practice and it can successfully handle large problem instances.