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Artykuły w czasopismach na temat "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.