Network Reconstruction Based on Evolutionary-Game Data via Compressive Sensing

Abstract

Evolutionary games model a common type of interactions in a variety of complex, networked, natural systems and social systems. Given such a system, uncovering the interacting structure of the underlying network is key to understanding its collective dynamics. Based on compressive sensing, we develop an efficient approach to reconstructing complex networks under game-based interactions from small amounts of data. The method is validated by using a variety of model networks and by conducting an actual experiment to reconstruct a social network. While most existing methods in this area assume oscillator networks that generate continuous-time data, our work successfully demonstrates that the extremely challenging problem of reverse engineering of complex networks can also be addressed even when the underlying dynamical processes are governed by realistic, evolutionary-game type of interactions in discrete time. In many fields of science and engineering, one encounters the situation where the system of interest is composed of networked elements, called nodes, but the pattern of the node-to-node interaction or the network topology is totally unknown. It is desirable and of significant interest to uncover the network topology based on time series of certain observable quantities extracted from experiments or observations. Examples of potential applications abound: reconstruction of gene-regulatory networks based on expression data in systems biology [1][2][3][4], extraction of various functional networks in the human brain from activation data in neuroscience [5][6][7][8], and uncovering organizational networks based on discrete data or information in social science and homeland defense. In the past few years, the problem of network reconstruction has received growing attention [9][10][11][12][13][14][15][16]. Most existing works were based, however, on networks of oscillators whose dynamics are mathematically described by coupled, continuous differential equations. In particular, either some knowledge about the dynamical evolution of the underlying networked system is needed [9][10][11] or long, oscillatory signals in continuous time are required [12][13][14][15][16]. The advantage of availing oneself of continuous-time data is lost for networks in social, economic, and even biological sciences where node-to-node interactions are governed by evolutionary-game types of dynamics [17][18][19][20][21]. In addition to being discrete, the available data may be sporadic and the amount may be small. To our knowledge, the problem of reconstructing the full topology of a network based on discrete and ''rare'' data remains outstanding [22].In this paper, we articulate a general method of addressing the problem of how to uncover network topology using evolutionary-game data based on compressive sensing, a recently developed paradigm for sparse-signal reconstruction [23][24][25][26][27][28] with broad applications ranging from image compression/reconstruction to the analysis of large-scale sensor-network data. Although convex opti...

Connecting Patterns Inspire Link Prediction in Complex Networks

“…Comparing with (10), the definitions of the two metrics are completely different, resulting in little correlation between them. Figure 3 shows PNR and the score distributions of existing and nonexisting links for USair network by CN method.…”

“…For example, analyzing the data of Facebook and Twitter helps find lost friends by only counting their common friends [6,7] and recommendation systems in online stores [8,9]. Restricted by instrument accuracy and other obstacles, we only obtain a small fraction or a snapshot of the complete networks [10,11], promoting us to filter the information in complex networks [12][13][14]. Link prediction is a straightforward approach to retrieve networks by predicting missing links and distinguishing spurious links [15][16][17].…”

Network Dynamics as an Inverse Problem

“…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.…”

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.…”

“…In general, two steps are followed in reconstructing the topology of sparsely connected dynamical networks: (i) recovering local structures centered at each node by a e-mail: kfcao163@163.com optimization methods such as compressed sensing [12,14], the lasso [19], regression and Bayesian inference [15]; (ii) assembling networks from these local structures. This node-based reconstruction (NR) approach may miss some useful information.…”