Dynamic Directed Network Representation Learning Based On Motif

Most of the existing researches on network subgraphs are statistical methods based on motif(or graphlet)detection and counting.It is difficult to combine the structure characteristics of subgraphs with the corresponding statistical characteristics effectively,and it is difficult to realize the effective characterization of network characteristics.In addition,most of the current research on large-scale complex networks is limited to static undirected networks,while most of the networks in the actual scene are dynamic directed networks,such as transportation networks,biological gene networks,financial networks,etc.,which lack sufficient theoretical analysis methods.Therefore,it is of great theoretical research value and practical significance to design a network representation learning method that can effectively extract the network structure characteristics,synthesize the local neighborhood information and global topology information of the network,and accurately characterize the characteristics of the directed dynamic network.Based on the classical cluster expansion representation of gas system in statistical thermodynamics,this paper constructs the relationship mapping from particle cluster to network motif,and deduces the partition function of directed network based on subgraph structure.Furthermore,the expression of thermodynamic variables of dynamic network is deduced,including network motif entropy,network motif energy and dynamic network temperature,so as to construct a dynamic directed network thermodynamic framework based on motif representation.In addition,this paper also introduces the global alignment kernel function based on the dynamic time warping framework,combines the structural characteristics of the motif with the statistical characteristics of the network,proposes the entropy graph kernel method based on the network motif,and studies and constructs the entropy kernel matrix representation.In order to further visualize the network dynamic evolution state,a kernel principal component analysis method based on network motif entropy is proposed.In the aspect of network dynamic evolution,the validity and superiority of the method are fully proved by comparing with the von Neumann thermodynamics framework method.In addition,compared with the traditional network statistical measurement method and the kernel method based on von Neumann entropy,the experiment has achieved better performance in multiple financial networks,gene networks,collaborative networks.