Reconstruction of Complex Network based on the Noise via QR Decomposition and Compressed Sensing

Lixiang Li,Haipeng Peng,Jürgen Kurths,Yixian Yang,Dafei Xu

doi:10.1038/s41598-017-15181-3

Abstract

It is generally known that the states of network nodes are stable and have strong correlations in a linear network system. We find that without the control input, the method of compressed sensing can not succeed in reconstructing complex networks in which the states of nodes are generated through the linear network system. However, noise can drive the dynamics between nodes to break the stability of the system state. Therefore, a new method integrating QR decomposition and compressed sensing is proposed to solve the reconstruction problem of complex networks under the assistance of the input noise. The state matrix of the system is decomposed by QR decomposition. We construct the measurement matrix with the aid of Gaussian noise so that the sparse input matrix can be reconstructed by compressed sensing. We also discover that noise can build a bridge between the dynamics and the topological structure. Experiments are presented to show that the proposed method is more accurate and more efficient to reconstruct four model networks and six real networks by the comparisons between the proposed method and only compressed sensing. In addition, the proposed method can reconstruct not only the sparse complex networks, but also the dense complex networks.

Highlights

Disadvantage of their approaches was that enough data were needed to be observed
Different with the existing methods that considered enough data were needed to achieve the reconstruction and the noise often harmed the network reconstruction, we discovered that less measurement data were required by the proposed QR-CS method to reconstruct the network after adding the Gaussian noise, which would increase the success rate of network reconstruction
By the discretization of the continuous variable, the model of complex networks generated by the linear system was transformed into a mathematical form that could be solved by the theory of compressed sensing

Summary

Introduction

How to reduce measurement data to achieve accurate network reconstruction is an important research problem. For the network reconstruction with less measurement data, the compressed sensing is an efficient method and it only acquires a smaller amount of sample data to recover the sparse signal. Wang et al.[22] proposed the reconstruction of complex networks based on the evolutionary game data via compressed sensing. This paper presents a new method to solve the reconstruction problem of complex networks whose node states are generated by the linear network system. We decompose the state matrix of the linear system by QR decomposition, construct the measurement matrix by Gaussian noise, and reconstruct the input sparse matrix based on compressed sensing. The proposed approach can efficiently reconstruct both the sparse and dense networks. We discover that only less measurement data are required by the proposed method to reconstruct the network after adding the Gaussian noise, which will increase the success rate of network reconstruction

Objectives

Methods

Results

Conclusion