A lot of combinatorial objects have a natural bialgebra structure. In this paper, we prove that the vector space spanned by labeled simple graphs is a bialgebra with the conjunction product and the unshuffle coproduct...A lot of combinatorial objects have a natural bialgebra structure. In this paper, we prove that the vector space spanned by labeled simple graphs is a bialgebra with the conjunction product and the unshuffle coproduct. In fact, it is a Hopf algebra since it is graded connected. The main conclusions are that the vector space spanned by labeled simple graphs arising from the unshuffle coproduct is a Hopf algebra and that there is a Hopf homomorphism from permutations to label simple graphs.展开更多
Numerous works prove that existing neighbor-averaging graph neural networks(GNNs)cannot efficiently catch structure features,and many works show that injecting structure,distance,position,or spatial features can signi...Numerous works prove that existing neighbor-averaging graph neural networks(GNNs)cannot efficiently catch structure features,and many works show that injecting structure,distance,position,or spatial features can significantly improve the performance of GNNs,however,injecting high-level structure and distance into GNNs is an intuitive but untouched idea.This work sheds light on this issue and proposes a scheme to enhance graph attention networks(GATs)by encoding distance and hop-wise structure statistics.Firstly,the hop-wise structure and distributional distance information are extracted based on several hop-wise ego-nets of every target node.Secondly,the derived structure information,distance information,and intrinsic features are encoded into the same vector space and then added together to get initial embedding vectors.Thirdly,the derived embedding vectors are fed into GATs,such as GAT and adaptive graph diffusion network(AGDN)to get the soft labels.Fourthly,the soft labels are fed into correct and smooth(C&S)to conduct label propagation and get final predictions.Experiments show that the distance and hop-wise structures encoding enhanced graph attention networks(DHSEGATs)achieve a competitive result.展开更多
The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlat...The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlation between abnormal connectivities and dementia disorders.However,it is challenging to access considerable amounts of brain functional network data,which hinders the widespread application of data-driven models in dementia diagnosis.In this study,a novel distribution-regularized adversarial graph auto-Encoder(DAGAE)with transformer is proposed to generate new fake brain functional networks to augment the brain functional network dataset,improving the dementia diagnosis accuracy of data-driven models.Specifically,the label distribution is estimated to regularize the latent space learned by the graph encoder,which canmake the learning process stable and the learned representation robust.Also,the transformer generator is devised to map the node representations into node-to-node connections by exploring the long-term dependence of highly-correlated distant brain regions.The typical topological properties and discriminative features can be preserved entirely.Furthermore,the generated brain functional networks improve the prediction performance using different classifiers,which can be applied to analyze other cognitive diseases.Attempts on the Alzheimer’s Disease Neuroimaging Initiative(ADNI)dataset demonstrate that the proposed model can generate good brain functional networks.The classification results show adding generated data can achieve the best accuracy value of 85.33%,sensitivity value of 84.00%,specificity value of 86.67%.The proposed model also achieves superior performance compared with other related augmentedmodels.Overall,the proposedmodel effectively improves cognitive disease diagnosis by generating diverse brain functional networks.展开更多
A graph G is said to be one modulo N-difference mean graph if there is an injective function f from the vertex set of G to the set , where N is the natural number and q is the number of edges of G and f induces a bije...A graph G is said to be one modulo N-difference mean graph if there is an injective function f from the vertex set of G to the set , where N is the natural number and q is the number of edges of G and f induces a bijection from the edge set of G to given by and the function f is called a one modulo N-difference mean labeling of G. In this paper, we show that the graphs such as arbitrary union of paths, , ladder, slanting ladder, diamond snake, quadrilateral snake, alternately quadrilateral snake, , , , , friendship graph and admit one modulo N-difference mean labeling.展开更多
为进一步优化重叠社区检测算法,提出了一种新的基于度和节点聚类系数的节点重要性定义,按照节点重要性降序更新节点,固定节点更新策略,提高社区检测的稳定性。在此基础上,提出了一种基于图嵌入和多标签传播的重叠社区检测算法(overlappi...为进一步优化重叠社区检测算法,提出了一种新的基于度和节点聚类系数的节点重要性定义,按照节点重要性降序更新节点,固定节点更新策略,提高社区检测的稳定性。在此基础上,提出了一种基于图嵌入和多标签传播的重叠社区检测算法(overlapping community detection based on graph embedding and multi-label propagation algorithm,OCD-GEMPA)。该算法结合node2vec模型对节点进行低维向量表示,构建节点之间的权重值矩阵,根据权重值计算标签归属系数,据此选择标签,避免了随机选择问题。在真实数据集和人工合成数据集上对该算法进行实验验证。实验结果表明,与其他重叠社区检测算法相比,OCD-GEMPA在EQ和NMI这两个指标都有明显提升,具有更好的准确性和稳定性。展开更多
针对学术论文在学科领域内进行层次标签分类问题,提出了一种基于知识增强的语义表示与图注意力网络的文本层次标签分类(text hierarchical label classification based on enhanced representation through knowledge integration and g...针对学术论文在学科领域内进行层次标签分类问题,提出了一种基于知识增强的语义表示与图注意力网络的文本层次标签分类(text hierarchical label classification based on enhanced representation through knowledge integration and graph attention networks, GETHLC)模型。首先,通过层次标签抽取模块提取学科领域下层次标签的结构特征,并通过预训练模型对学术论文的摘要、标题和抽取后的层次标签结构特征进行嵌入;然后,在分类阶段基于层次标签的结构分层构造层次分类器,将学术论文逐层分类至最符合的类别中。在大规模中文科学文献数据集CSL上进行的实验结果表明,与基准的ERNIE模型相比,GETHLC模型的准确率、召回率和F1值分别提升了5.78、4.31和5.02百分点。展开更多
文摘A lot of combinatorial objects have a natural bialgebra structure. In this paper, we prove that the vector space spanned by labeled simple graphs is a bialgebra with the conjunction product and the unshuffle coproduct. In fact, it is a Hopf algebra since it is graded connected. The main conclusions are that the vector space spanned by labeled simple graphs arising from the unshuffle coproduct is a Hopf algebra and that there is a Hopf homomorphism from permutations to label simple graphs.
文摘Numerous works prove that existing neighbor-averaging graph neural networks(GNNs)cannot efficiently catch structure features,and many works show that injecting structure,distance,position,or spatial features can significantly improve the performance of GNNs,however,injecting high-level structure and distance into GNNs is an intuitive but untouched idea.This work sheds light on this issue and proposes a scheme to enhance graph attention networks(GATs)by encoding distance and hop-wise structure statistics.Firstly,the hop-wise structure and distributional distance information are extracted based on several hop-wise ego-nets of every target node.Secondly,the derived structure information,distance information,and intrinsic features are encoded into the same vector space and then added together to get initial embedding vectors.Thirdly,the derived embedding vectors are fed into GATs,such as GAT and adaptive graph diffusion network(AGDN)to get the soft labels.Fourthly,the soft labels are fed into correct and smooth(C&S)to conduct label propagation and get final predictions.Experiments show that the distance and hop-wise structures encoding enhanced graph attention networks(DHSEGATs)achieve a competitive result.
基金This paper is partially supported by the British Heart Foundation Accelerator Award,UK(AA\18\3\34220)Royal Society International Exchanges Cost Share Award,UK(RP202G0230)+9 种基金Hope Foundation for Cancer Research,UK(RM60G0680)Medical Research Council Confidence in Concept Award,UK(MC_PC_17171)Sino-UK Industrial Fund,UK(RP202G0289)Global Challenges Research Fund(GCRF),UK(P202PF11)LIAS Pioneering Partnerships Award,UK(P202ED10)Data Science Enhancement Fund,UK(P202RE237)Fight for Sight,UK(24NN201)Sino-UK Education Fund,UK(OP202006)Biotechnology and Biological Sciences Research Council,UK(RM32G0178B8)LIAS Seed Corn,UK(P202RE969).
文摘The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlation between abnormal connectivities and dementia disorders.However,it is challenging to access considerable amounts of brain functional network data,which hinders the widespread application of data-driven models in dementia diagnosis.In this study,a novel distribution-regularized adversarial graph auto-Encoder(DAGAE)with transformer is proposed to generate new fake brain functional networks to augment the brain functional network dataset,improving the dementia diagnosis accuracy of data-driven models.Specifically,the label distribution is estimated to regularize the latent space learned by the graph encoder,which canmake the learning process stable and the learned representation robust.Also,the transformer generator is devised to map the node representations into node-to-node connections by exploring the long-term dependence of highly-correlated distant brain regions.The typical topological properties and discriminative features can be preserved entirely.Furthermore,the generated brain functional networks improve the prediction performance using different classifiers,which can be applied to analyze other cognitive diseases.Attempts on the Alzheimer’s Disease Neuroimaging Initiative(ADNI)dataset demonstrate that the proposed model can generate good brain functional networks.The classification results show adding generated data can achieve the best accuracy value of 85.33%,sensitivity value of 84.00%,specificity value of 86.67%.The proposed model also achieves superior performance compared with other related augmentedmodels.Overall,the proposedmodel effectively improves cognitive disease diagnosis by generating diverse brain functional networks.
文摘A graph G is said to be one modulo N-difference mean graph if there is an injective function f from the vertex set of G to the set , where N is the natural number and q is the number of edges of G and f induces a bijection from the edge set of G to given by and the function f is called a one modulo N-difference mean labeling of G. In this paper, we show that the graphs such as arbitrary union of paths, , ladder, slanting ladder, diamond snake, quadrilateral snake, alternately quadrilateral snake, , , , , friendship graph and admit one modulo N-difference mean labeling.
文摘为进一步优化重叠社区检测算法,提出了一种新的基于度和节点聚类系数的节点重要性定义,按照节点重要性降序更新节点,固定节点更新策略,提高社区检测的稳定性。在此基础上,提出了一种基于图嵌入和多标签传播的重叠社区检测算法(overlapping community detection based on graph embedding and multi-label propagation algorithm,OCD-GEMPA)。该算法结合node2vec模型对节点进行低维向量表示,构建节点之间的权重值矩阵,根据权重值计算标签归属系数,据此选择标签,避免了随机选择问题。在真实数据集和人工合成数据集上对该算法进行实验验证。实验结果表明,与其他重叠社区检测算法相比,OCD-GEMPA在EQ和NMI这两个指标都有明显提升,具有更好的准确性和稳定性。
文摘针对学术论文在学科领域内进行层次标签分类问题,提出了一种基于知识增强的语义表示与图注意力网络的文本层次标签分类(text hierarchical label classification based on enhanced representation through knowledge integration and graph attention networks, GETHLC)模型。首先,通过层次标签抽取模块提取学科领域下层次标签的结构特征,并通过预训练模型对学术论文的摘要、标题和抽取后的层次标签结构特征进行嵌入;然后,在分类阶段基于层次标签的结构分层构造层次分类器,将学术论文逐层分类至最符合的类别中。在大规模中文科学文献数据集CSL上进行的实验结果表明,与基准的ERNIE模型相比,GETHLC模型的准确率、召回率和F1值分别提升了5.78、4.31和5.02百分点。
