A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower tha...A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower than that of ECP method in several order of magnitude.展开更多
Forecasting 3-dimensional skeleton-based human poses from the historical sequence is a classic task,which shows enormous potential in robotics,computer vision,and graphics.Currently,the state-of-theart methods resort ...Forecasting 3-dimensional skeleton-based human poses from the historical sequence is a classic task,which shows enormous potential in robotics,computer vision,and graphics.Currently,the state-of-theart methods resort to graph convolutional networks(GCNs)to access the relationships of human joint pairs to formulate this problem.However,human action involves complex interactions among multiple joints,which presents a higher-order correlation overstepping the pairwise(2-order)connection of GCNs.Moreover,joints are typically activated by the parent joint,rather than driving their parent joints,whereas in existing methods,this specific direction of information transmission is ignored.In this work,we propose a novel hybrid directed hypergraph convolution network(H-DHGCN)to model the high-order relationships of the human skeleton with directionality.Specifically,our H-DHGCN mainly involves 2 core components.One is the static directed hypergraph,which is pre-defined according to the human body structure,to effectively leverage the natural relations of human joints.The second is dynamic directed hypergraph(D-DHG).D-DHG is learnable and can be constructed adaptively,to learn the unique characteristics of the motion sequence.In contrast to the typical GCNs,our method brings a richer and more refined topological representation of skeleton data.On several large-scale benchmarks,experimental results show that the proposed model consistently surpasses the latest techniques.展开更多
The concepts of the undirected and directed decompositions are introduced for a hyperedge.Then, the recursive formulas of the underected decomposition set SD(m) and directed decomposition set SPD(m) are derived for an...The concepts of the undirected and directed decompositions are introduced for a hyperedge.Then, the recursive formulas of the underected decomposition set SD(m) and directed decomposition set SPD(m) are derived for an m-vertex hyperedge.Furthermore,the recursive formulas of their cardinalities|SD(m)|and |SPD(m)| are yielded.展开更多
We obtain the sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor.By using the technique of the representation associate matrix of a tensor and the associate directed graph ...We obtain the sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor.By using the technique of the representation associate matrix of a tensor and the associate directed graph of the matrix,the equality cases of the bounds are completely characterized by graph theory methods.Applying these bounds to a nonnegative irreducible matrix or a connected graph(digraph),we can improve the results of L.H.You,Y.J.Shu,and P.Z.Yuan[Linear Multilinear Algebra,2017,65(1):113-128],and obtain some new or known results.Applying these bounds to a uniform hypergraph,we obtain some new results and improve some known results of X.Y.Yuan,M.Zhang,and M.Lu[Linear Algebra Appl.,2015,484:540-549].Finally,we give a characterization of a strongly connected/c-uniform directed hypergraph,and obtain some new results by applying these bounds to a uniform directed hypergraph.展开更多
文摘A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower than that of ECP method in several order of magnitude.
基金supported in part by the National Natural Science Foundation of China(62306141)in part by the Jiangsu Funding Program for Excellent Postdoctoral Talent(2022ZB269)+2 种基金in part by the Natural Science Foundation of Jiangsu Province(BK20220939)in part by the China Postdoctoral Science Foundation(2022M721629)in part by Research Project of University Natural Science Fund of Jiangsu Province(22KJB520002).
文摘Forecasting 3-dimensional skeleton-based human poses from the historical sequence is a classic task,which shows enormous potential in robotics,computer vision,and graphics.Currently,the state-of-theart methods resort to graph convolutional networks(GCNs)to access the relationships of human joint pairs to formulate this problem.However,human action involves complex interactions among multiple joints,which presents a higher-order correlation overstepping the pairwise(2-order)connection of GCNs.Moreover,joints are typically activated by the parent joint,rather than driving their parent joints,whereas in existing methods,this specific direction of information transmission is ignored.In this work,we propose a novel hybrid directed hypergraph convolution network(H-DHGCN)to model the high-order relationships of the human skeleton with directionality.Specifically,our H-DHGCN mainly involves 2 core components.One is the static directed hypergraph,which is pre-defined according to the human body structure,to effectively leverage the natural relations of human joints.The second is dynamic directed hypergraph(D-DHG).D-DHG is learnable and can be constructed adaptively,to learn the unique characteristics of the motion sequence.In contrast to the typical GCNs,our method brings a richer and more refined topological representation of skeleton data.On several large-scale benchmarks,experimental results show that the proposed model consistently surpasses the latest techniques.
文摘The concepts of the undirected and directed decompositions are introduced for a hyperedge.Then, the recursive formulas of the underected decomposition set SD(m) and directed decomposition set SPD(m) are derived for an m-vertex hyperedge.Furthermore,the recursive formulas of their cardinalities|SD(m)|and |SPD(m)| are yielded.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11571123,11871040,11971180)the Guangdong Provincial Natural Science Foundation(No.2015A030313377)Guangdong Engineering Research Center for Data Science.
文摘We obtain the sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor.By using the technique of the representation associate matrix of a tensor and the associate directed graph of the matrix,the equality cases of the bounds are completely characterized by graph theory methods.Applying these bounds to a nonnegative irreducible matrix or a connected graph(digraph),we can improve the results of L.H.You,Y.J.Shu,and P.Z.Yuan[Linear Multilinear Algebra,2017,65(1):113-128],and obtain some new or known results.Applying these bounds to a uniform hypergraph,we obtain some new results and improve some known results of X.Y.Yuan,M.Zhang,and M.Lu[Linear Algebra Appl.,2015,484:540-549].Finally,we give a characterization of a strongly connected/c-uniform directed hypergraph,and obtain some new results by applying these bounds to a uniform directed hypergraph.
