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
The concepts of modified graphs of a composite graph with respect to two vertex-pairs and a hyperedge-decomposition are introduced,respectively.By applying them and thedirected hypergraph theory,the topological formul...The concepts of modified graphs of a composite graph with respect to two vertex-pairs and a hyperedge-decomposition are introduced,respectively.By applying them and thedirected hypergraph theory,the topological formulas for the parameter-extraction theorem andsubnetwork-extraction theorems are derived,and then the topological formulas for multiterminalfeedback networks are presented.In these formulas the parameters of the feedback subnetworkare separated from that of the fundamental subnetwork,so that it is convenient to find out theeffect of the feedback parameters.Furthermore,since one network is decomposed into two smallersubnetworks,the computing time complexity and space complexity can be reduced.展开更多
Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples.Recently,there have been several successful proposals to generalize graph neural networks to hypergraph neu...Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples.Recently,there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to exploit more com-plex relationships.In particular,the hypergraph collaborative networks yield superior results compared to other hypergraph neural net-works for various semi-supervised learning tasks.The collaborative network can provide high quality vertex embeddings and hyperedge embeddings together by formulating them as a joint optimization problem and by using their consistency in reconstructing the given hy-pergraph.In this paper,we aim to establish the algorithmic stability of the core layer of the collaborative network and provide generaliz--ation guarantees.The analysis sheds light on the design of hypergraph filters in collaborative networks,for instance,how the data and hypergraph filters should be scaled to achieve uniform stability of the learning process.Some experimental results on real-world datasets are presented to illustrate the theory.展开更多
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.
文摘The concepts of modified graphs of a composite graph with respect to two vertex-pairs and a hyperedge-decomposition are introduced,respectively.By applying them and thedirected hypergraph theory,the topological formulas for the parameter-extraction theorem andsubnetwork-extraction theorems are derived,and then the topological formulas for multiterminalfeedback networks are presented.In these formulas the parameters of the feedback subnetworkare separated from that of the fundamental subnetwork,so that it is convenient to find out theeffect of the feedback parameters.Furthermore,since one network is decomposed into two smallersubnetworks,the computing time complexity and space complexity can be reduced.
基金Ng was supported in part by Hong Kong Research Grant Council General Research Fund(GRF),China(Nos.12300218,12300519,117201020,17300021,CRF C1013-21GF,C7004-21GF and Joint NSFC-RGC NHKU76921)Wu is supported by National Natural Science Foundation of China(No.62206111)+3 种基金Young Talent Support Project of Guangzhou Association for Science and Technology,China(No.QT-2023-017)Guangzhou Basic and Applied Basic Research Foundation,China(No.2023A04J1058)Fundamental Research Funds for the Central Universities,China(No.21622326)China Postdoctoral Science Foundation(No.2022M721343).
文摘Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples.Recently,there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to exploit more com-plex relationships.In particular,the hypergraph collaborative networks yield superior results compared to other hypergraph neural net-works for various semi-supervised learning tasks.The collaborative network can provide high quality vertex embeddings and hyperedge embeddings together by formulating them as a joint optimization problem and by using their consistency in reconstructing the given hy-pergraph.In this paper,we aim to establish the algorithmic stability of the core layer of the collaborative network and provide generaliz--ation guarantees.The analysis sheds light on the design of hypergraph filters in collaborative networks,for instance,how the data and hypergraph filters should be scaled to achieve uniform stability of the learning process.Some experimental results on real-world datasets are presented to illustrate the theory.
