Reconstruction of Complex Time-varying Weighted Networks Based on LASSO

Abstract

Network reconstruction is significant in a variety of domains including physics, biology, engineering and social science. Although a lot of effort has been put into static network reconstructions, time-varying networks are rarely studied. Existing studies of time-varying networks usually assume nodes' dynamics to be linear or consider nodes' nonlinear dynamics as prior knowledge. In this paper, identification of time-varying weighted networks is discussed under the condition where network topology, link weights and nodes' nonlinear dynamics are all unknown or unavailable. In fact, networks in real world are naturally sparse which enables the transformation from network reconstruction problem into sparse signal recovering, so that $l_{1}$ regularization can be effectively applicable. Based on the assumption that most natural networks can be mathematically expressed by only a few important analytical functions, we construct a function set consisting of both linear and nonlinear candidate functions. Then LASSO is applied to select the possible function assemblies from the proposed set and optimize the coefficients of the corresponding function terms in order to best describe time-varying structures as well as nodes' nonlinear dynamics. To prove the feasibility and effectiveness of this reconstruction method, both two complex models are testified in networks of different sizes. And this method shows potential ability applying to a wide range of dynamical time-varying networks.