Robust Reconstruction of Complex Networks from Sparse Data

Abstract

Reconstructing complex networks from measurable data is a fundamental problem for understanding and controlling collective dynamics of complex networked systems. However, a significant challenge arises when we attempt to decode structural information hidden in limited amounts of data accompanied by noise and in the presence of inaccessible nodes. Here, we develop a general framework for robust reconstruction of complex networks from sparse and noisy data. Specifically, we decompose the task of reconstructing the whole network into recovering local structures centered at each node. Thus, the natural sparsity of complex networks ensures a conversion from the local structure reconstruction into a sparse signal reconstruction problem that can be addressed by using the lasso, a convex optimization method. We apply our method to evolutionary games, transportation and communication processes taking place in a variety of model and real complex networks, finding that universal high reconstruction accuracy can be achieved from sparse data in spite of noise in time series and missing data of partial nodes. Our approach opens new routes to the network reconstruction problem and has potential applications in a wide range of fields. 89.75.Fb, 05.45.Tp Complex networked systems are common in many fields [1][2][3]. The need to ascertain collective dynamics of such systems to control them is shared among different scientific communities [4][5][6]. Much evidence has demonstrated that interaction patterns among dynamical elements captured by a complex network play deterministic roles in collective dynamics [7]. It is thus imperative to study a complex networked system as a whole rather than study each component separately to offer a comprehensive understanding of the whole system [8]. However, we are often incapable of directly accessing network structures; instead, only limited observable data are available [9], raising the need for network reconstruction approaches to uncovering network structures from data. Network reconstruction, the inverse problem, is challenging because structural information is hidden in measurable data in an unknown manner and the solution space of all possible structural configurations is of extremely high dimension. So far a number of approaches have been proposed to address the inverse problem [4,5,[9][10][11][12][13][14][15][16][17]. However, accurate and robust reconstruction of large complex networks is still a challenging problem, especially given limited measurements disturbed by noise and unexpected factors.In this letter, we develop a general framework to reconcile the contradiction between the robustness of reconstructing complex networks and limits on our ability to access sufficient amounts of data required by conventional approaches. The key lies in converting the network reconstruction problem into a sparse signal reconstruction problem that can be addressed by exploiting the lasso, a convex optimization algorithm [18,19]. In particular, reconstructing the whole network structure can be...

Network Dynamics as an Inverse Problem

“…Previous studies on inferring structural connections from time series have focused on the reconstruction of networks with known local and coupling functions [22,[68][69][70]73,74]. Such prior knowledge reduces the problem of inferring connections to a standard linear algebra problem, where one has to solve a linear system of equations to reveal the network connections, cf.…”

“…Still, researchers often select particular models for h i , involving known functions and specific types of interactions to explain the network dynamics [22,69,70,73,74]. Subsequently, based on these models, one may reconstruct the network connectivity from recorded measurements.…”

“…In particular, knowing the actual parameters and functions generating the network dynamics reduces the problem of inferring network structural connections to just fitting a collection of unknown parameters (in this case the connections) to measured data [34,35,40,[68][69][70][71][72][73]. Such approaches are especially reliable when estimating connections from time series [68][69][70][71][72][73][74], even in the presence of challenging dynamics (e.g.…”

Image Converting into Complex Networks : Scale- Level Segmentation Approach

“…One might find out that several papers are devoted to conversion of diverse data into networks , for example [18,[20][21][22]. However, there have been so far few works which treat images as complex networks in problems of image analysis and recognition [23,24].…”

Global and partitioned reconstructions of undirected complex networks

“…How to infer the interaction topology from the collective dynamics of a complex network has recently attracted extensive attention. To address this inverse problem, many methods have been proposed and they usually show robust and high performance with appropriate observations [9,10,11,12,13,14,15,16,17,18,19,20,21]. In view of the issues regarding measurement cost, however, further studies to improve the prediction efficiency are necessary.…”