Network reconstruction based on compressive sensing

Abstract

To identify the structure of networks is essential for analysis of complex networks. This paper transforms network reconstruction to be a signal recovery problem by means of compressive sensing. In the literature, the sensing matrix is determined by the network dynamic and measured states of nodes, which might violates the restriction on the coherence of the sensing matrix for exact recovery. This paper proposes random projection and zero component analysis to preprocess the sensing matrix in order to reduce the coherence of the sensing matrix. These two data whitening techniques are implemented in three different ways with different space complexity required, performing transformation on diagonal blocks, on multiple diagonal blocks and on the whole of the sensing matrix. Numerical simulations suggest that the latter method are effective to improve the quality of the reconstructed networks and comparisons are made among these methods and the ways they are implemented.