Research On Geometric And Sparse Representation Learning For Complex Network

Networks widely exist in the real world,such as social networks,transportation net-works,protein networks,etc.The graph is an intuitive way to represent a complex network.However,the use of graphs to represent complex networks faces the following two problems: In the tasks to analyze networks,graphs are difficult to be processed via vector-based data analysis models? In the tasks to infer hidden networks,graphs contain too many parameters to be estimated,and thus it is difficult to infer the networks from limited network dynamics data.In view of the above two problems,this thesis starts from the ideas of network geometry and sparse constraints,and focuses on two topics,network distribution representation learning for network analysis and network compression repre-sentation learning for hidden network inference.The main studies and contributions in this thesis are as follows:1)To address the distortion problem in graph embedding by proximity preservation,we propose a basic solution,which is to constrain the curve of the embedding manifold via a curvature regularization.This thesis proposes a novel angle-based section curvature for graph embedding,called ABS curvature,and correspondingly proposes a curvature regularization to induce ”flat” embedding manifolds with low distortion.In this thesis,two efficient variants of the curvature regularization are proposed to solve the scalability problem,and the optimization strategy of the curvature regularization is designed.Ex-perimental results show that the proposed curvature regularizations generally improve the performance of existing graph embedding methods.2)To address the two fundamental weaknesses of the aggregation function of mes-sage passing neural network(MPNN),namely the loss of neighborhood structure and the difficulty in obtaining long-range dependence,this thesis proposes a novel idea,which is the use of the continuous hidden geometric space behind the graph to assist MPNN ag-gregation.This thesis proposes a novel geometric aggregation scheme,which can extract or “reconstruct” the missing information(i.e.,neighborhood structure and long-range de-pendence)from the embedding space of the graph,and design several geometric graph convolutional networks(Geom-GCNs)to implement the geometric aggregation scheme.Experimental results show that Geom-GCNs have higher prediction accuracy than the state-of-the-art baselines,especially in disassortative networks.3)To address the ill-posed problem in hidden network inference,this thesis pro-poses a network compression representation method for hidden network inference based on group sparse Bayesian learning,and applies it to active surveillance,which predicts the dynamics of the entire complex network by monitoring a small number of key nodes.This thesis proposes a novel importance measure,the value,to indicate the monitoring priority of nodes in the dynamics prediction task,and theoretically analyzes from both a priori and a posteriori perspectives.Based on this measure,this thesis designs a sen-tinel network mining algorithm(SNMA)based on a backward selection strategy,in which group sparse Bayesian learning is employed to estimate the compressed representation of hidden networks in linear continuous systems and logistic discrete systems.This thesis solves the scalability problem of SNMA and extends SNMA to nonlinear dynamic sys-tems through basis function embedding to deal with complex diffusion mechanisms.The experimental results show that the SNMA algorithm can effectively learn the compres-sion representation of the hidden network,and SNMA outperforms the state-of-the-art baselines in active surveillance.4)To address the ill-posed problem in dynamical hidden network inference,this the-sis proposes a dynamical network compression representation learning method.With a similar dynamics function of the original dynamical network,the compression represen-tation greatly reduces the number of parameters to be estimated,which enables us to infer dynamical social contact networks from limited dynamics data.Taking the spread predic-tion of infectious diseases as a background,this thesis proposes a tensor deconvolution sparse coding framework,integrating infectious disease models and multiple heteroge-neous data sources,so as to jointly infer a compression representation of dynamical social contacts network.On four specific infectious diseases datasets(H1N1,mumps,seasonal influenza,and varicella),this thesis empirically verifies the effectiveness of the proposed framework and analyzes infectious disease prevention and control strategies,such as clos-ing schools and distributing vaccines,by spread simulation.