基于稀疏贝叶斯学习的复杂网络拓扑估计

摘要

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.%提出了一种噪声环境下复杂网络拓扑估计方法,仅利用含噪时间序列估计未知结构混沌系统的动力学方程和参数,以及由混沌系统组成的复杂网络的拓扑结构、节点动力学方程、所有参数、节点间耦合方向和耦合强度.通过采用动力学方程的统一形式,将动力系统方程结构和参数估计看成线性回归问题的系数估计,该估计问题利用贝叶斯压缩传感的信号重建算法求解,含噪信号的模型重建使用相关向量机方法,即通过稀疏贝叶斯学习求解稀疏欠定线性方程得到上面提到的可估计对象.以单个Lorenz系统及由200个Lorenz系统组成的无标度网络为例说明方法的有效性.仿真结果表明,提出的方法对噪声有很强的鲁棒性,收敛速度快,稳态误差极小,克服了最小二乘估计方法收敛速度慢、稳态误差大以及压缩传感估计方法对噪声鲁棒性不强的缺点.