Artykuły w czasopismach: „Hypergraph-structure”

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Xu, Jinhuan, Liang Xiao, and Jingxiang Yang. "Unified Low-Rank Subspace Clustering with Dynamic Hypergraph for Hyperspectral Image." Remote Sensing 13, no. 7 (2021): 1372. http://dx.doi.org/10.3390/rs13071372.

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Low-rank representation with hypergraph regularization has achieved great success in hyperspectral imagery, which can explore global structure, and further incorporate local information. Existing hypergraph learning methods only construct the hypergraph by a fixed similarity matrix or are adaptively optimal in original feature space; they do not update the hypergraph in subspace-dimensionality. In addition, the clustering performance obtained by the existing k-means-based clustering methods is unstable as the k-means method is sensitive to the initialization of the cluster centers. In order to address these issues, we propose a novel unified low-rank subspace clustering method with dynamic hypergraph for hyperspectral images (HSIs). In our method, the hypergraph is adaptively learned from the low-rank subspace feature, which can capture a more complex manifold structure effectively. In addition, we introduce a rotation matrix to simultaneously learn continuous and discrete clustering labels without any relaxing information loss. The unified model jointly learns the hypergraph and the discrete clustering labels, in which the subspace feature is adaptively learned by considering the optimal dynamic hypergraph with the self-taught property. The experimental results on real HSIs show that the proposed methods can achieve better performance compared to eight state-of-the-art clustering methods.

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Feng, Yifan, Haoxuan You, Zizhao Zhang, Rongrong Ji, and Yue Gao. "Hypergraph Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 3558–65. http://dx.doi.org/10.1609/aaai.v33i01.33013558.

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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.

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Liu, Jian, Dong Chen, Jingyan Li, and Jie Wu. "Neighborhood hypergraph model for topological data analysis." Computational and Mathematical Biophysics 10, no. 1 (2022): 262–80. http://dx.doi.org/10.1515/cmb-2022-0142.

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Abstract Hypergraph, as a generalization of the notions of graph and simplicial complex, has gained a lot of attention in many fields. It is a relatively new mathematical model to describe the high-dimensional structure and geometric shapes of data sets. In this paper,we introduce the neighborhood hypergraph model for graphs and combine the neighborhood hypergraph model with the persistent (embedded) homology of hypergraphs. Given a graph,we can obtain a neighborhood complex introduced by L. Lovász and a filtration of hypergraphs parameterized by aweight function on the power set of the vertex set of the graph. Theweight function can be obtained by the construction fromthe geometric structure of graphs or theweights on the vertices of the graph. We show the persistent theory of such filtrations of hypergraphs. One typical application of the persistent neighborhood hypergraph is to distinguish the planar square structure of cisplatin and transplatin. Another application of persistent neighborhood hypergraph is to describe the structure of small fullerenes such as C20. The bond length and the number of adjacent carbon atoms of a carbon atom can be derived from the persistence diagram. Moreover, our method gives a highly matched stability prediction (with a correlation coefficient 0.9976) of small fullerene molecules.

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Yang, Zhe, Liangkui Xu, and Lei Zhao. "Multimodal Feature Fusion Based Hypergraph Learning Model." Computational Intelligence and Neuroscience 2022 (May 16, 2022): 1–13. http://dx.doi.org/10.1155/2022/9073652.

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Hypergraph learning is a new research hotspot in the machine learning field. The performance of the hypergraph learning model depends on the quality of the hypergraph structure built by different feature extraction methods as well as its incidence matrix. However, the existing models are all hypergraph structures built based on one feature extraction method, with limited feature extraction and abstract expression ability. This paper proposed a multimodal feature fusion method, which firstly built a single modal hypergraph structure based on different feature extraction methods, and then extended the hypergraph incidence matrix and weight matrix of different modals. The extended matrices fuse the multimodal abstract feature and an expanded Markov random walk range during model learning, with stronger feature expression ability. However, the extended multimodal incidence matrix has a high scale and high computational cost. Therefore, the Laplacian matrix fusion method was proposed, which performed Laplacian matrix transformation on the incidence matrix and weight matrix of every model, respectively, and then conducted a weighted superposition on these Laplacian matrices for subsequent model training. The tests on four different types of datasets indicate that the hypergraph learning model obtained after multimodal feature fusion has a better classification performance than the single modal model. After Laplace matrix fusion, the average time can be reduced by about 40% compared with the extended incidence matrix, the classification performance can be further improved, and the index F1 can be improved by 8.4%.

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Mahmood Shuker, Faiza. "Improved Blockchain Network Performance using Hypergraph Structure." Journal of Engineering and Applied Sciences 14, no. 2 (2019): 5579–84. http://dx.doi.org/10.36478/jeasci.2019.5579.5584.

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Peng, Hao, Cheng Qian, Dandan Zhao, Ming Zhong, Jianmin Han, and Wei Wang. "Targeting attack hypergraph networks." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 7 (2022): 073121. http://dx.doi.org/10.1063/5.0090626.

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In modern systems, from brain neural networks to social group networks, pairwise interactions are not sufficient to express higher-order relationships. The smallest unit of their internal function is not composed of a single functional node but results from multiple functional nodes acting together. Therefore, researchers adopt the hypergraph to describe complex systems. The targeted attack on random hypergraph networks is still a problem worthy of study. This work puts forward a theoretical framework to analyze the robustness of random hypergraph networks under the background of a targeted attack on nodes with high or low hyperdegrees. We discovered the process of cascading failures and the giant connected cluster (GCC) of the hypergraph network under targeted attack by associating the simple mapping of the factor graph with the hypergraph and using percolation theory and generating function. On random hypergraph networks, we do Monte-Carlo simulations and find that the theoretical findings match the simulation results. Similarly, targeted attacks are more effective than random failures in disintegrating random hypergraph networks. The threshold of the hypergraph network grows as the probability of high hyperdegree nodes being deleted increases, indicating that the network’s resilience becomes more fragile. When considering real-world scenarios, our conclusions are validated by real-world hypergraph networks. These findings will help us understand the impact of the hypergraph’s underlying structure on network resilience.

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Xu, Xixia, Qi Zou, and Xue Lin. "Adaptive Hypergraph Neural Network for Multi-Person Pose Estimation." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 3 (2022): 2955–63. http://dx.doi.org/10.1609/aaai.v36i3.20201.

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This paper proposes a novel two-stage hypergraph-based framework, dubbed ADaptive Hypergraph Neural Network (AD-HNN) to estimate multiple human poses from a single image, with a keypoint localization network and an Adaptive-Pose Hypergraph Neural Network (AP-HNN) added onto the former network. For providing better guided representations of AP-HNN, we employ a Semantic Interaction Convolution (SIC) module within the initial localization network to acquire more explicit predictions. Build upon this, we design a novel adaptive hypergraph to represent a human body for capturing high-order semantic relations among different joints. Notably, it can adaptively adjust the relations between joints and seek the most reasonable structure for the variable poses to benefit the keypoint localization. These two stages are combined to be trained in an end-to-end fashion. Unlike traditional Graph Convolutional Networks (GCNs) that are based on a fixed tree structure, AP-HNN can deal with ambiguity in human pose estimation. Experimental results demonstrate that the AD-HNN achieves state-of-the-art performance both on the MS-COCO, MPII and CrowdPose datasets.

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Huang, Yuan, Liping Wang, Xueying Wang, and Wei An. "Joint Probabilistic Hypergraph Matching Labeled Multi-Bernoulli Filter for Rigid Target Tracking." Applied Sciences 10, no. 1 (2019): 99. http://dx.doi.org/10.3390/app10010099.

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The likelihood determined by the distance between measurements and predicted states of targets is widely used in many filters for data association. However, if the actual motion model of targets is not coincided with the preset dynamic motion model, this criterion will lead to poor performance when close-space targets are tracked. For rigid target tracking task, the structure of rigid targets can be exploited to improve the data association performance. In this paper, the structure of the rigid target is represented as a hypergraph, and the problem of data association is formulated as a hypergraph matching problem. However, the performance of hypergraph matching degrades if there are missed detections and clutter. To overcome this limitation, we propose a joint probabilistic hypergraph matching labeled multi-Bernoulli (JPHGM-LMB) filter with all undetected cases being considered. In JPHGM-LMB, the likelihood is built based on group structure rather than the distance between predicted states and measurements. Consequently, the probability of each target associated with each measurement (joint association probabilities) can be obtained. Then, the structure information is integrated into LMB filter by revising each single target likelihood with joint association probabilities. However, because all undetected cases is considered, proposed approach is usable in real time only for a limited number of targets. Extensive simulations have demonstrated the significant performance improvement of our proposed method.

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Kosian, David A., and Leon A. Petrosyan. "Two-Level Cooperative Game on Hypergraph." Contributions to Game Theory and Management 14 (2021): 227–35. http://dx.doi.org/10.21638/11701/spbu31.2021.17.

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In the paper, the cooperative game with a hypergraph communication structure is considered. For this class of games, a new allocation rule was proposed by splitting the original game into a game between hyperlinks and games within them. The communication possibilities are described by the hypergraph in which the nodes are players and hyperlinks are the communicating subgroups of players. The game between hyperlinks and between players in each hyperlink is described. The payoff of each player is influenced by the actions of other players dependent on the distance between them on hypergraph. Constructed characteristic functions based on cooperative behaviour satisfy the convexity property. The results are shown by the example.

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Siriwong, Pinkaew, and Ratinan Boonklurb. "k-Zero-Divisor and Ideal-Based k-Zero-Divisor Hypergraphs of Some Commutative Rings." Symmetry 13, no. 11 (2021): 1980. http://dx.doi.org/10.3390/sym13111980.

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Let R be a commutative ring with nonzero identity and k≥2 be a fixed integer. The k-zero-divisor hypergraph Hk(R) of R consists of the vertex set Z(R,k), the set of all k-zero-divisors of R, and the hyperedges of the form {a1,a2,a3,…,ak}, where a1,a2,a3,…,ak are k distinct elements in Z(R,k), which means (i) a1a2a3⋯ak=0 and (ii) the products of all elements of any (k−1) subsets of {a1,a2,a3,…,ak} are nonzero. This paper provides two commutative rings so that one of them induces a family of complete k-zero-divisor hypergraphs, while another induces a family of k-partite σ-zero-divisor hypergraphs, which illustrates unbalanced or asymmetric structure. Moreover, the diameter and the minimum length of all cycles or girth of the family of k-partite σ-zero-divisor hypergraphs are determined. In addition to a k-zero-divisor hypergraph, we provide the definition of an ideal-based k-zero-divisor hypergraph and some basic results on these hypergraphs concerning a complete k-partite k-uniform hypergraph, a complete k-uniform hypergraph, and a clique.

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Manimaran, P., and K. Duraiswamy. "Identifying Overlying Group of People through Clustering." International Journal of Information Technology and Web Engineering 7, no. 4 (2012): 50–60. http://dx.doi.org/10.4018/jitwe.2012100104.

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Folksonomies like Delicious and LastFm are modeled as multilateral (user-resource-tag) hypergraphs for studying their network properties. Detecting communities of similar nodes from such networks is a challenging problem. Most existing algorithms for community detection in folksonomies assign unique communities to nodes, whereas in reality, users have multiple relevant interests and same resource is often tagged with semantically different tags. Few attempts to perceive overlapping communities work on forecasts of hypergraph, which results in momentous loss of information contained in original tripartite structure. Propose first algorithm to detect overlapping communities in folksonomies using complete hypergraph structure. The authors’ algorithm converts a hypergraph into its parallel line graph, using measures of hyperedge similarity, whereby any community detection algorithm on unipartite graphs can be used to produce intersecting communities in folksonomy. Through extensive experiments on synthetic as well as real folksonomy data, demonstrate that proposed algorithm can detect better community structures as compared to existing state-of-the-art algorithms for folksonomies.

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ARNDT, TIMOTHY, SHI-KUO CHANG, and ANGELA GUERCIO. "FORMAL SPECIFICATION AND PROTOTYPING OF MULTIMEDIA APPLICATIONS." International Journal of Software Engineering and Knowledge Engineering 10, no. 04 (2000): 377–409. http://dx.doi.org/10.1142/s0218194000000250.

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Multimedia systems incorporating hyperlinks and user interaction can be prototyped using TAOML, an extension of HTML. TAOML is used to define a Teleaction Object (TAO) which is a multimedia object with associated hypergraph structure and knowledge structure The hypergraph structure supports the effective presentation and efficient communication of multimedia information. In this paper, a formal specification methodology for TAOs using Symbol Relation (SR) grammars is described. An attributed SR grammar is then introduced in order to associate knowledge with the TAO. The limitations to achieve an efficient parser are given. The grammatical formalism allows for validation and verification of the system specification. This methodology provides a principled approach to specify, verify, validate and prototype multimedia applications.

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HAXELL, PENNY, and LOTHAR NARINS. "A Stability Theorem for Matchings in Tripartite 3-Graphs." Combinatorics, Probability and Computing 27, no. 5 (2018): 774–93. http://dx.doi.org/10.1017/s0963548318000147.

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It follows from known results that every regular tripartite hypergraph of positive degree, with n vertices in each class, has matching number at least n/2. This bound is best possible, and the extremal configuration is unique. Here we prove a stability version of this statement, establishing that every regular tripartite hypergraph with matching number at most (1 + ϵ)n/2 is close in structure to the extremal configuration, where ‘closeness’ is measured by an explicit function of ϵ.

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Vertigan, Dirk, and Geoff Whittle. "Recognizing Polymatroids Associated with Hypergraphs." Combinatorics, Probability and Computing 2, no. 4 (1993): 519–30. http://dx.doi.org/10.1017/s0963548300000882.

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Two natural classes of polymatroids can be associated with hypergraphs: the so-called Boolean and hypergraphic polymatroids. Boolean polymatroids carry virtually all the structure of hypergraphs; hypergraphic polymatroids generalize graphic matroids. This paper considers algorithmic problems associated with recognizing members of these classes. Let k be a fixed positive integer and assume that the k-polymatroid ρ is presented via a rank oracle. We present an algorithm that determines in polynomial time whether ρ is Boolean, and if it is, finds the hypergraph. We also give an algorithm that decides in polynomial time whether ρ is the hypergraphic polymatroid associated with a given hypergraph. Other structure-theoretic results are also given.

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Hodkinson, Ian, and Martin Otto. "Finite Conformal Hypergraph Covers and Gaifman Cliques in Finite Structures." Bulletin of Symbolic Logic 9, no. 3 (2003): 387–405. http://dx.doi.org/10.2178/bsl/1058448678.

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AbstractWe provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques—thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms, we show that every finite hypergraph admits a bisimilar cover by a finite conformal hypergraph. In terms of relational structures, we show that every finite relational structure admits a guarded bisimilar cover by a finite structure whose Gaifman cliques are guarded. One of our applications answers an open question about a clique constrained strengthening of the extension property for partial automorphisms (EPPA) of Hrushovski, Herwig and Lascar. A second application provides an alternative proof of the finite model property (FMP) for the clique guarded fragment of first-order logic CGF, by reducing (finite) satisfiability in CGF to (finite) satisfiability in the guarded fragment, GF.

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Ancona, Massimo, and Leila De Floriani. "A hypergraph-based hierarchial data structure and its applications." Advances in Engineering Software (1978) 11, no. 1 (1989): 2–11. http://dx.doi.org/10.1016/0141-1195(89)90030-2.

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Ali Rasheed Alrowily, Ibtesam. "Hypergraphs: Application in Food networks." JOURNAL OF ADVANCES IN MATHEMATICS 21 (March 13, 2022): 50–57. http://dx.doi.org/10.24297/jam.v21i.9207.

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A hypergraph is a generalization of a graph since, in a graph an edge relates only a pair of points, but the edges of a hypergraph known as hyperedges can relate groups of more than two points. The representation of complex systems as graphs is appropriate for the study of certain problems. We give several examples of social, biological, ecological and technological systems where the use of graphs gives very limited information about the structure of the system. We propose to use hypergraphs to represent these systems.

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Liu, Yang, He Zhao, and Qiao Xin Zhang. "A Multi-Scale Data Fusion-Based Method for Modular Decomposition." Applied Mechanics and Materials 220-223 (November 2012): 2794–98. http://dx.doi.org/10.4028/www.scientific.net/amm.220-223.2794.

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Facing the module division for the product life cycle, this paper presents a hierarchical module decomposition based on the multi-scale data fusion, use the hypergraph and multi-scale theory to divide modules into classification, and realize hierarchical expression of modules. First use the process model of modular design process established by associated hypergraph, which provide the mapping network basis for user needs, then reference the hypergraph on the formal description of the parts information to establish the parts associated matrix, and achieve primary modules division through calculation of parts relevance. Secondly reference multi-scale data fusion technology to map associated matrix from components to modules layer based on primary module structure, and establish the primary modules associated matrix, then complete the second grade modular division. Finally, the case analysis shows the scientific and practical of the method.

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Hu, Yu, and Hongmin Cai. "Hypergraph-Supervised Deep Subspace Clustering." Mathematics 9, no. 24 (2021): 3259. http://dx.doi.org/10.3390/math9243259.

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Auto-encoder (AE)-based deep subspace clustering (DSC) methods aim to partition high-dimensional data into underlying clusters, where each cluster corresponds to a subspace. As a standard module in current AE-based DSC, the self-reconstruction cost plays an essential role in regularizing the feature learning. However, the self-reconstruction adversely affects the discriminative feature learning of AE, thereby hampering the downstream subspace clustering. To address this issue, we propose a hypergraph-supervised reconstruction to replace the self-reconstruction. Specifically, instead of enforcing the decoder in the AE to merely reconstruct samples themselves, the hypergraph-supervised reconstruction encourages reconstructing samples according to their high-order neighborhood relations. By the back-propagation training, the hypergraph-supervised reconstruction cost enables the deep AE to capture the high-order structure information among samples, facilitating the discriminative feature learning and, thus, alleviating the adverse effect of the self-reconstruction cost. Compared to current DSC methods, relying on the self-reconstruction, our method has achieved consistent performance improvement on benchmark high-dimensional datasets.

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Huang, Hong, Meili Chen, and Yule Duan. "Dimensionality Reduction of Hyperspectral Image Using Spatial-Spectral Regularized Sparse Hypergraph Embedding." Remote Sensing 11, no. 9 (2019): 1039. http://dx.doi.org/10.3390/rs11091039.

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Many graph embedding methods are developed for dimensionality reduction (DR) of hyperspectral image (HSI), which only use spectral features to reflect a point-to-point intrinsic relation and ignore complex spatial-spectral structure in HSI. A new DR method termed spatial-spectral regularized sparse hypergraph embedding (SSRHE) is proposed for the HSI classification. SSRHE explores sparse coefficients to adaptively select neighbors for constructing the dual sparse hypergraph. Based on the spatial coherence property of HSI, a local spatial neighborhood scatter is computed to preserve local structure, and a total scatter is computed to represent the global structure of HSI. Then, an optimal discriminant projection is obtained by possessing better intraclass compactness and interclass separability, which is beneficial for classification. Experiments on Indian Pines and PaviaU hyperspectral datasets illustrated that SSRHE effectively develops a better classification performance compared with the traditional spectral DR algorithms.

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Xu, Yunxia, Linzhang Lu, Qilong Liu, and Zhen Chen. "Hypergraph-Regularized Lp Smooth Nonnegative Matrix Factorization for Data Representation." Mathematics 11, no. 13 (2023): 2821. http://dx.doi.org/10.3390/math11132821.

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Nonnegative matrix factorization (NMF) has been shown to be a strong data representation technique, with applications in text mining, pattern recognition, image processing, clustering and other fields. In this paper, we propose a hypergraph-regularized Lp smooth nonnegative matrix factorization (HGSNMF) by incorporating the hypergraph regularization term and the Lp smoothing constraint term into the standard NMF model. The hypergraph regularization term can capture the intrinsic geometry structure of high dimension space data more comprehensively than simple graphs, and the Lp smoothing constraint term may yield a smooth and more accurate solution to the optimization problem. The updating rules are given using multiplicative update techniques, and the convergence of the proposed method is theoretically investigated. The experimental results on five different data sets show that the proposed method has a better clustering effect than the related state-of-the-art methods in the vast majority of cases.

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Yi, Sudo, and Deok-Sun Lee. "Structure of international trade hypergraphs." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 10 (2022): 103402. http://dx.doi.org/10.1088/1742-5468/ac946f.

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Abstract We study the structure of the international trade hypergraph consisting of triangular hyperedges representing the exporter–importer–product relationship. Measuring the mean hyperdegree of the adjacent vertices, we first find its behaviors different from those in the pairwise networks and explain the origin by tracing the relation between the hyperdegree and the pairwise degree. To interpret the observed hyperdegree correlation properties in the context of trade strategies, we decompose the correlation into two components by identifying one with the background correlation remnant even in the exponential random hypergraphs preserving the given empirical hyperdegree sequence. The other component characterizes the net correlation and reveals the bias of the exporters of low hyperdegree towards the importers of high hyperdegree and the products of low hyperdegree, which information is not readily accessible in the pairwise networks. Our study demonstrates the power of the hypergraph approach in the study of real-world complex systems and offers a theoretical framework.

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Ma, Jichao, Chunyu Du, Weifeng Liu, and Yanjiang Wang. "Numerical Simulation of Higher-Order Nonlinearity of Human Brain Functional Connectivity Using Hypergraph p-Laplacian." Mathematics 9, no. 18 (2021): 2345. http://dx.doi.org/10.3390/math9182345.

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Unravelling how the human brain structure gives rise to function is a central question in neuroscience and remains partially answered. Recent studies show that the graph Laplacian of the human brain’s structural connectivity (SC) plays a dominant role in shaping the pattern of resting-state functional connectivity (FC). The modeling of FC using the graph Laplacian of the brain’s SC is limited, owing to the sparseness of the Laplacian matrix. It is unable to model the negative functional correlations. We extended the graph Laplacian to the hypergraph p-Laplacian in order to describe better the nonlinear and high-order relations between SC and FC. First we estimated those possible links showing negative correlations between the brain areas shared across subjects by statistical analysis. Then we presented a hypergraph p-Laplacian model by embedding the two matrices referring to the sign of the correlations between the brain areas relying on the brain structural connectome. We tested the model on two experimental connectome datasets and evaluated the predicted FC by estimating its Pearson correlation with the empirical FC matrices. The results showed that the proposed diffusion model based on hypergraph p-Laplacian can predict functional correlations more accurately than the models using graph Laplacian as well as hypergraph Laplacian.

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Xu, Haozheng, Yiwen Zhang, Xing Jin, Jingrui Wang, and Zhen Wang. "The Evolution of Cooperation in Multigames with Uniform Random Hypergraphs." Mathematics 11, no. 11 (2023): 2409. http://dx.doi.org/10.3390/math11112409.

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How to explain the emergence of cooperative behavior remains a significant problem. As players may hold diverse perceptions on a particular dilemma, the concept of multigames has been introduced. Therefore, a multigame is studied within various binary networks. Since group structures are common in human society and a person can participate in multiple groups, this paper studies an evolutionary multigame with high-order interaction properties. For this purpose, a uniform random hypergraph is adopted as the network structure, allowing players to interact with all nodes in the same hyperedge. First, we investigate the effect of the multigame payoff matrix differences on the evolution of cooperation and find that increasing the differences in the payoff matrix promotes cooperation on the hypergraph network. Second, we discover that an increase in the average hyperdegree of the hypergraph network promotes network reciprocity, wherein high-hyperdegree nodes influence surrounding nodes to form a cooperator cluster. Conversely, groups with a low hyperdegree are more susceptible to betrayal, leading to a decline in cooperation.

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Hu, Feng, Kuo Tian, and Zi-Ke Zhang. "Identifying Vital Nodes in Hypergraphs Based on Von Neumann Entropy." Entropy 25, no. 9 (2023): 1263. http://dx.doi.org/10.3390/e25091263.

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Hypergraphs have become an accurate and natural expression of high-order coupling relationships in complex systems. However, applying high-order information from networks to vital node identification tasks still poses significant challenges. This paper proposes a von Neumann entropy-based hypergraph vital node identification method (HVC) that integrates high-order information as well as its optimized version (semi-SAVC). HVC is based on the high-order line graph structure of hypergraphs and measures changes in network complexity using von Neumann entropy. It integrates s-line graph information to quantify node importance in the hypergraph by mapping hyperedges to nodes. In contrast, semi-SAVC uses a quadratic approximation of von Neumann entropy to measure network complexity and considers only half of the maximum order of the hypergraph’s s-line graph to balance accuracy and efficiency. Compared to the baseline methods of hyperdegree centrality, closeness centrality, vector centrality, and sub-hypergraph centrality, the new methods demonstrated superior identification of vital nodes that promote the maximum influence and maintain network connectivity in empirical hypergraph data, considering the influence and robustness factors. The correlation and monotonicity of the identification results were quantitatively analyzed and comprehensive experimental results demonstrate the superiority of the new methods. At the same time, a key non-trivial phenomenon was discovered: influence does not increase linearly as the s-line graph orders increase. We call this the saturation effect of high-order line graph information in hypergraph node identification. When the order reaches its saturation value, the addition of high-order information often acts as noise and affects propagation.

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Hu Feng, Zhao Hai-Xing, He Jia-Bei, Li Fa-Xu, Li Shu-Ling, and Zhang Zi-Ke. "An evolving model for hypergraph-structure-based scientific collaboration networks." Acta Physica Sinica 62, no. 19 (2013): 198901. http://dx.doi.org/10.7498/aps.62.198901.

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SUN, Xue-Dong. "Directed Hypergraph Based and Resource Constrained Enterprise Process Structure Optimization." Journal of Software 17, no. 1 (2006): 59. http://dx.doi.org/10.1360/jos170059.

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Long, Jane Holsapple, and Sarah Crown Rundell. "The Hodge structure of the coloring complex of a hypergraph." Discrete Mathematics 311, no. 20 (2011): 2164–73. http://dx.doi.org/10.1016/j.disc.2011.06.034.

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KOPONEN, VERA. "BINARY PRIMITIVE HOMOGENEOUS SIMPLE STRUCTURES." Journal of Symbolic Logic 82, no. 1 (2017): 183–207. http://dx.doi.org/10.1017/jsl.2016.51.

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AbstractSuppose that ${\cal M}$ is countable, binary, primitive, homogeneous, and simple. We prove that the SU-rank of the complete theory of ${\cal M}$ is 1 and hence 1-based. It follows that ${\cal M}$ is a random structure. The conclusion that ${\cal M}$ is a random structure does not hold if the binarity condition is removed, as witnessed by the generic tetrahedron-free 3-hypergraph. However, to show that the generic tetrahedron-free 3-hypergraph is 1-based requires some work (it is known that it has the other properties) since this notion is defined in terms of imaginary elements. This is partly why we also characterize equivalence relations which are definable without parameters in the context of ω-categorical structures with degenerate algebraic closure. Another reason is that such characterizations may be useful in future research about simple (nonbinary) homogeneous structures.

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Devezas, José, and Sérgio Nunes. "Hypergraph-of-entity." Open Computer Science 9, no. 1 (2019): 103–27. http://dx.doi.org/10.1515/comp-2019-0006.

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AbstractModern search is heavily powered by knowledge bases, but users still query using keywords or natural language. As search becomes increasingly dependent on the integration of text and knowledge, novel approaches for a unified representation of combined data present the opportunity to unlock new ranking strategies. We have previously proposed the graph-of-entity as a purely graph-based representation and retrieval model, however this model would scale poorly. We tackle the scalability issue by adapting the model so that it can be represented as a hypergraph. This enables a significant reduction of the number of (hyper)edges, in regard to the number of nodes, while nearly capturing the same amount of information. Moreover, such a higher-order data structure, presents the ability to capture richer types of relations, including nary connections such as synonymy, or subsumption. We present the hypergraph-of-entity as the next step in the graph-of-entity model, where we explore a ranking approach based on biased random walks. We evaluate the approaches using a subset of the INEX 2009 Wikipedia Collection. While performance is still below the state of the art, we were, in part, able to achieve a MAP score similar to TF-IDF and greatly improve indexing efficiency over the graph-of-entity.

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31

Lu, Zhiwu, and Yuxin Peng. "Latent Semantic Learning by Efficient Sparse Coding with Hypergraph Regularization." Proceedings of the AAAI Conference on Artificial Intelligence 25, no. 1 (2011): 411–16. http://dx.doi.org/10.1609/aaai.v25i1.7896.

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This paper presents a novel latent semantic learning algorithm for action recognition. Through efficient sparse coding, we can learn latent semantics (i.e. high-level features) from a large vocabulary of abundant mid-level features (i.e. visual keywords). More importantly, we can capture the manifold structure hidden among mid-level features by incorporating hypergraph regularization into sparse coding. The learnt latent semantics can further be readily used for action recognition by defining a histogram intersection kernel. Different from the traditional latent semantic analysis based on topic models, our sparse coding method with hypergraph regularization can exploit the manifold structure hidden among mid-level features for latent semantic learning, which results in compact but discriminative high-level features for action recognition. We have tested our method on the commonly used KTH action dataset and the unconstrained YouTube action dataset. The experimental results show the superior performance of our method.

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32

Aguiar, Manuela, Christian Bick, and Ana Dias. "Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony." Nonlinearity 36, no. 9 (2023): 4641–73. http://dx.doi.org/10.1088/1361-6544/ace39f.

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Abstract Network interactions that are nonlinear in the state of more than two nodes—also known as higher-order interactions—can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to elucidate the existence and stability of (cluster) synchronization patterns in network dynamical systems with higher-order interactions. More specifically, we define robust synchrony subspace for coupled cell hypernetworks whose coupling structure is determined by an underlying hypergraph and describe those spaces for general such hypernetworks. Since a hypergraph can be equivalently represented as a bipartite graph between its nodes and hyperedges, we relate the synchrony subspaces of a hypernetwork to balanced colourings of the corresponding incidence digraph.

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Xi, Zhengtao, Tongqiang Liu, Haifeng Shi, and Zhuqing Jiao. "Hypergraph representation of multimodal brain networks for patients with end-stage renal disease associated with mild cognitive impairment." Mathematical Biosciences and Engineering 20, no. 2 (2023): 1882–902. http://dx.doi.org/10.3934/mbe.2023086.

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<abstract><p>The structure and function of brain networks (BN) may be altered in patients with end-stage renal disease (ESRD). However, there are relatively few attentions on ESRD associated with mild cognitive impairment (ESRDaMCI). Most studies focus on the pairwise relationships between brain regions, without taking into account the complementary information of functional connectivity (FC) and structural connectivity (SC). To address the problem, a hypergraph representation method is proposed to construct a multimodal BN for ESRDaMCI. First, the activity of nodes is determined by connection features extracted from functional magnetic resonance imaging (fMRI) (i.e., FC), and the presence of edges is determined by physical connections of nerve fibers extracted from diffusion kurtosis imaging (DKI) (i.e., SC). Then, the connection features are generated through bilinear pooling and transformed into an optimization model. Next, a hypergraph is constructed according to the generated node representation and connection features, and the node degree and edge degree of the hypergraph are calculated to obtain the hypergraph manifold regularization (HMR) term. The HMR and <bold><italic>L</italic></bold><sub>1</sub> norm regularization terms are introduced into the optimization model to achieve the final hypergraph representation of multimodal BN (HRMBN). Experimental results show that the classification performance of HRMBN is significantly better than that of several state-of-the-art multimodal BN construction methods. Its best classification accuracy is 91.0891%, at least 4.3452% higher than that of other methods, verifying the effectiveness of our method. The HRMBN not only achieves better results in ESRDaMCI classification, but also identifies the discriminative brain regions of ESRDaMCI, which provides a reference for the auxiliary diagnosis of ESRD.</p></abstract>

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34

Mythili, R., Revathi Venkataraman, and T. Sai Raj. "An attribute-based lightweight cloud data access control using hypergraph structure." Journal of Supercomputing 76, no. 8 (2020): 6040–64. http://dx.doi.org/10.1007/s11227-019-03119-7.

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Klonowski, Wlodzimierz. "Probabilistic-topological theory of systems with discrete interactions: II. Calculation of the hypergraph probabilistic representation; the difference a posteriori algorithm." Canadian Journal of Physics 66, no. 12 (1988): 1061–68. http://dx.doi.org/10.1139/p88-170.

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The scheme of calculations, which subsequently will be called the difference a posteriori algorithm (or just DAPOST), is formulated in a general and rigorous manner to make its application to different systems with discrete interactions (SDI) possible. The DAPOST enables one to calculate important probabilistic characteristics of SDI while having only general information about its composition and interactions between system elements. The DAPOST is easily adaptable to very different physicochemical and biophysical systems, especially to the problems of element aggregation and binding. When applied together with a hypergraph representation of the SDI under consideration the DAPOST allows construction of equivalent probabilistic representations of the hypergraph modelling the SDI, in this way often considerably simplifying calculations of the structure–property relationships of the SDI.

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Ibrahim, Rania, and David F. Gleich. "Local hypergraph clustering using capacity releasing diffusion." PLOS ONE 15, no. 12 (2020): e0243485. http://dx.doi.org/10.1371/journal.pone.0243485.

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Local graph clustering is an important machine learning task that aims to find a well-connected cluster near a set of seed nodes. Recent results have revealed that incorporating higher order information significantly enhances the results of graph clustering techniques. The majority of existing research in this area focuses on spectral graph theory-based techniques. However, an alternative perspective on local graph clustering arises from using max-flow and min-cut on the objectives, which offer distinctly different guarantees. For instance, a new method called capacity releasing diffusion (CRD) was recently proposed and shown to preserve local structure around the seeds better than spectral methods. The method was also the first local clustering technique that is not subject to the quadratic Cheeger inequality by assuming a good cluster near the seed nodes. In this paper, we propose a local hypergraph clustering technique called hypergraph CRD (HG-CRD) by extending the CRD process to cluster based on higher order patterns, encoded as hyperedges of a hypergraph. Moreover, we theoretically show that HG-CRD gives results about a quantity called motif conductance, rather than a biased version used in previous experiments. Experimental results on synthetic datasets and real world graphs show that HG-CRD enhances the clustering quality.

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Liu, Yang, He Zhao, and Qiao Xin Zhang. "The Multi-Scale Modeling Technique for Modular Variant Design." Advanced Materials Research 538-541 (June 2012): 3110–14. http://dx.doi.org/10.4028/www.scientific.net/amr.538-541.3110.

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Facing the modularization of existing product variant design requirements, this paper presents a multi-scale modeling technology. Discuss the process of the change scope of the parts and modules according to the needs of the user, so divide the modular product model into process model, modules model and parts model. Use associated hypergraph describe the constraint relation between different stages of modular design process, the process model provides network basis for user needs mapping. Use the structured hypergraph to conduct formal description of parts and modules information and establish structured model; then fuse constraint information of the structure model based on the multi-scale data fusion technology, and provide constraint data source for changed coefficients of the components and modules. Finally, the case analysis shows the scientific and practical of the method.

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Sun, Ling, Yuan Rao, Xiangbo Zhang, Yuqian Lan, and Shuanghe Yu. "MS-HGAT: Memory-Enhanced Sequential Hypergraph Attention Network for Information Diffusion Prediction." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 4 (2022): 4156–64. http://dx.doi.org/10.1609/aaai.v36i4.20334.

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Predicting the diffusion cascades is a critical task to understand information spread on social networks. Previous methods usually focus on the order or structure of the infected users in a single cascade, thus ignoring the global dependencies of users and cascades, limiting the performance of prediction. Current strategies to introduce social networks only learn the social homogeneity among users, which is not enough to describe their interaction preferences, let alone the dynamic changes. To address the above issues, we propose a novel information diffusion prediction model named Memory-enhanced Sequential Hypergraph Attention Networks (MS-HGAT). Specifically, to introduce the global dependencies of users, we not only take advantages of their friendships, but also consider their interactions at the cascade level. Furthermore, to dynamically capture user' preferences, we divide the diffusion hypergraph into several sub graphs based on timestamps, develop Hypergraph Attention Networks to learn the sequential hypergraphs, and connect them with gated fusion strategy. In addition, a memory-enhanced embedding lookup module is proposed to capture the learned user representations into the cascade-specific embedding space, thus highlighting the feature interaction within the cascade. The experimental results over four realistic datasets demonstrate that MS-HGAT significantly outperforms the state-of-the-art diffusion prediction models in both Hits@K and MAP@k metrics.

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Xiao, Guanchen, Jinzhi Liao, Zhen Tan, Yiqi Yu, and Bin Ge. "Hyperbolic Directed Hypergraph-Based Reasoning for Multi-Hop KBQA." Mathematics 10, no. 20 (2022): 3905. http://dx.doi.org/10.3390/math10203905.

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The target of the multi-hop knowledge base question-answering task is to find answers of some factoid questions by reasoning across multiple knowledge triples in the knowledge base. Most of the existing methods for multi-hop knowledge base question answering based on a general knowledge graph ignore the semantic relationship between each hop. However, modeling the knowledge base as a directed hypergraph has the problems of sparse incidence matrices and asymmetric Laplacian matrices. To make up for the deficiency, we propose a directed hypergraph convolutional network modeled on hyperbolic space, which can better deal with the sparse structure, and effectively adapt to the problem of an asymmetric incidence matrix of directed hypergraphs modeled on a knowledge base. We propose an interpretable KBQA model based on the hyperbolic directed hypergraph convolutional neural network named HDH-GCN which can update relation semantic information hop-by-hop and pays attention to different relations at different hops. The model can improve the accuracy of the multi-hop knowledge base question-answering task, and has application value in text question answering, human–computer interactions and other fields. Extensive experiments on benchmarks—PQL, MetaQA—demonstrate the effectiveness and universality of our HDH-GCN model, leading to state-of-the-art performance.

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40

Fan, Youping, Jingjiao Li, Dai Zhang, Jie Pi, Jiahan Song, and Guo Zhao. "Supporting Sustainable Maintenance of Substations under Cyber-Threats: An Evaluation Method of Cybersecurity Risk for Power CPS." Sustainability 11, no. 4 (2019): 982. http://dx.doi.org/10.3390/su11040982.

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In the increasingly complex cyber-environment, appropriate sustainable maintenance of substation auto systems (SASs) can lead to many positive effects on power cyber-physical systems (CPSs). Evaluating the cybersecurity risk of power CPSs is the first step in creating sustainable maintenance plans for SASs. In this paper, a mathematical framework for evaluating the cybersecurity risk of a power CPS is proposed considering both the probability of successful cyberattacks on SASs and their consequences for the power system. First, the cyberattacks and their countermeasures are introduced, and the probability of successful cyber-intruding on SASs is modeled from the defender’s perspective. Then, a modified hypergraph model of the SAS’s logical structure is established to quantitatively analyze the impacts of cyberattacks on an SAS. The impacts will ultimately act on the physical systems of the power CPS. The modified hypergraph model can describe more information than a graph or hypergraph model and potentially can analyze complex networks like CPSs. Finally, the feasibility and effectiveness of the proposed evaluation method is verified by the IEEE 14-bus system, and the test results demonstrate that this proposed method is more reasonable to assess the cybersecurity risk of power CPS compared with some other models.

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Li, Yiran, Renchi Yang, and Jieming Shi. "Efficient and Effective Attributed Hypergraph Clustering via K-Nearest Neighbor Augmentation." Proceedings of the ACM on Management of Data 1, no. 2 (2023): 1–23. http://dx.doi.org/10.1145/3589261.

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Hypergraphs are an omnipresent data structure used to represent high-order interactions among entities. Given a hypergraph H wherein nodes are associated with attributes, attributed hypergraph clustering (AHC) aims to partition the nodes in H into k disjoint clusters, such that intra-cluster nodes are closely connected and share similar attributes, while inter-cluster nodes are far apart and dissimilar. It is highly challenging to capture multi-hop connections via nodes or attributes on large attributed hypergraphs for accurate clustering. Existing AHC solutions suffer from issues of prohibitive computational costs, sub-par clustering quality, or both. In this paper, we present AHCKA, an efficient approach to AHC, which achieves state-of-the-art result quality via several algorithmic designs. Under the hood, AHCKA includes three key components: (i) a carefully-crafted K-nearest neighbor augmentation strategy for the optimized exploitation of attribute information on hypergraphs, (ii) a joint hypergraph random walk model to devise an effective optimization objective towards AHC, and (iii) a highly efficient solver with speedup techniques for the problem optimization. Extensive experiments, comparing AHCKA against 15 baselines over 8 real attributed hypergraphs, reveal that AHCKA is superior to existing competitors in terms of clustering quality, while often being up to orders of magnitude faster.

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Yang, Kai, Yong Long Jin, and Zhi Jun He. "A Briefest Feature Subset Selection Algorithm Based on Preference Attribute." Advanced Materials Research 774-776 (September 2013): 1816–22. http://dx.doi.org/10.4028/www.scientific.net/amr.774-776.1816.

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Concept lattice is the core data structure of formal concept analysis and represents the order relationship between the concepts iconically. Feature selection has been the focus of research in machine learning.And feature selection has been shown very effective in removing irrelevant and redundant features,also increasing efficiency in learning process and obtaining more intelligible learned results.This paper proposes a new briefest feature subset selection algorithm based on preference attribute on the basis of study of concept lattice theory. User can put forward a preference attribute according to their subjective experiences, all the briefest feature subsets containing the given attribute can be discovered by the algorithm. It firstly find some special concept pairs and calculate their waned-value hypergraph, then obtain the minimal transversal of the hypergraph as a result. A practical example proves the method is cogent and effective.

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Luqman, Anam, Muhammad Akram, and Ali N. A. Koam. "Granulation of Hypernetwork Models under the q-Rung Picture Fuzzy Environment." Mathematics 7, no. 6 (2019): 496. http://dx.doi.org/10.3390/math7060496.

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In this paper, we define q-rung picture fuzzy hypergraphs and illustrate the formation of granular structures using q-rung picture fuzzy hypergraphs and level hypergraphs. Further, we define the q-rung picture fuzzy equivalence relation and q-rung picture fuzzy hierarchical quotient space structures. In particular, a q-rung picture fuzzy hypergraph and hypergraph combine a set of granules, and a hierarchical structure is formed corresponding to the series of hypergraphs. The mappings between the q-rung picture fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of the universal set is more efficient through q-rung picture fuzzy hypergraphs and the q-rung picture fuzzy equivalence relation. We also present an arithmetic example and comparison analysis to signify the superiority and validity of our proposed model.

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Robert Jäschke, Robert, Beate Krause, Andreas Hotho, and Gerd Stumme. "Logsonomy — A Search Engine Folksonomy." Proceedings of the International AAAI Conference on Web and Social Media 2, no. 1 (2021): 192–93. http://dx.doi.org/10.1609/icwsm.v2i1.18646.

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In social bookmarking systems users describe bookmarks by keywords called tags. The structure behind these social systems, called folksonomies, can be viewed as a tripartite hypergraph of user, tag and resource nodes. This underlying network shows specific structural properties that explain its growth and the possibility of serendipitous exploration. Search engines filter the vast information of the web. Queries describe a user's information need. In response to the displayed results of the search engine, users click on the links of the result page as they expect the answer to be of relevance. The clickdata can be represented as a folksonomy in which queries are descriptions of clicked URLs. This poster analyzes the topological characteristics of the resulting tripartite hypergraph of queries, users and bookmarks of two query logs and compares it two a snapshot of the folksonomy del.icio.us.

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GANEA, E., D. D. BURDESCU, and M. BREZOVAN. "New Method to Detect Salient Objects in Image Segmentation using Hypergraph Structure." Advances in Electrical and Computer Engineering 11, no. 4 (2011): 111–16. http://dx.doi.org/10.4316/aece.2011.04018.

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Zheng, Xiaoyao, Yonglong Luo, Liping Sun, Xintao Ding, and Ji Zhang. "A novel social network hybrid recommender system based on hypergraph topologic structure." World Wide Web 21, no. 4 (2017): 985–1013. http://dx.doi.org/10.1007/s11280-017-0494-5.

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Golubski, Antonio J., Erik E. Westlund, John Vandermeer, and Mercedes Pascual. "Ecological Networks over the Edge: Hypergraph Trait-Mediated Indirect Interaction (TMII) Structure." Trends in Ecology & Evolution 31, no. 5 (2016): 344–54. http://dx.doi.org/10.1016/j.tree.2016.02.006.

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Qiu, Chunhua, Shaoyun Ge, Ting Yang, Jun Wei, and Guoxing Xiang. "Research on Power Generation Energy Sources Structure Adjustment Algorithm Based on HyperGraph." American Journal of Energy Engineering 7, no. 2 (2019): 49. http://dx.doi.org/10.11648/j.ajee.20190702.12.

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Konstantinova, E. V., and V. A. Skoroboratov. "Graph and hypergraph models of molecular structure: A comparative analysis of indices." Journal of Structural Chemistry 39, no. 6 (1998): 958–66. http://dx.doi.org/10.1007/bf02903615.

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Vasilyeva, Ekaterina, Miguel Romance, Ivan Samoylenko, et al. "Distances in Higher-Order Networks and the Metric Structure of Hypergraphs." Entropy 25, no. 6 (2023): 923. http://dx.doi.org/10.3390/e25060923.

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We explore the metric structure of networks with higher-order interactions and introduce a novel definition of distance for hypergraphs that extends the classic methods reported in the literature. The new metric incorporates two critical factors: (1) the inter-node distance within each hyperedge, and (2) the distance between hyperedges in the network. As such, it involves the computation of distances in a weighted line graph of the hypergraph. The approach is illustrated with several ad hoc synthetic hypergraphs, where the structural information unveiled by the novel metric is highlighted. Moreover, the method’s performance and effectiveness are shown through computations on large real-world hypergraphs, which indeed reveal new insights into the structural features of networks beyond pairwise interactions. Namely, using the new distance measure, we generalize the definitions of efficiency, closeness and betweenness centrality for the case of hypergraphs. Comparing the values of these generalized measures with their analogs calculated for the hypergraph clique projections, we show that our measures provide significantly different assessments on the characteristics (and roles) of the nodes from the information-transferability point of view. The difference is brighter for hypergraphs in which hyperedges of large sizes are frequent, and nodes relating to these hyperedges are rarely connected by other hyperedges of smaller sizes.

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