Estimating topology of complex networks based on sparse Bayesian learning

Abstract

We propose a method of estimating complex network topology with a noisy environment. Our method can estimate not only dynamical equation of the chaotic system and its parameters but also topology, the dynamical equation of each node, all the parameters, coupling direction and coupling strength of complex dynamical network composed of coupled unknown chaotic systems using only noisy time series. Estimating the system structure and parameter is regard as estimating the linear regression coefficients by reconstructing system with universal polynomial structure. Reconstruction algorithm of Bayesian compressive sensing is used for estimating the coefficients of regression polynomial. For the reconstruction from noisy time series we adopt relevance vector machine, namely we use sparse Bayesian learning to solve sparse undetermined linear equation to obtain the objects mentioned above. The Lorenz system and a scale free network composed of 200 Lorenz systems are provided to illustrate the efficiency. Simulation results show that our method improves the robust to noise compared with the compressive sensing and has fast convergence speed and tiny steady state error compared with the least square strategy.