Complex networks hosting binary-state dynamics can represent many phenomena in real world systems. Therefore, some approaches were proposed to reconstruct the structures of networks with binary-state dynamics. However...
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Complex networks hosting binary-state dynamics can represent many phenomena in real world systems. Therefore, some approaches were proposed to reconstruct the structures of networks with binary-state dynamics. However, they often hold two assumptions: 1) require a priori knowledge about which state is the active state, or one state is imposed as the active state;and 2) only one side of transition probability is utilized for network reconstruction. Many binary-state dynamics, such as cooperative/defective state in evolutionary game, agree/disagree of two competing opinions, it is hard to define which state is the active state, what's more, both sides of the transition probability depend on the states of neighbors. For this situation, if we only consider one side of transition probability, the reconstruction accuracy is greatly discounted because many data are not effectively used. By abandoning the two assumptions, we here develop a generalized statistical inference approach by exploiting the expectation-maximization algorithm to reconstruct networks. Our approach requires less information regarding the dynamics, indicating more potential applications. More importantly, our approach sufficiently mines the given data, the results on empirical and synthetic networks demonstrate the high-reconstruction accuracy. In addition, the method is parameter free and robust to the stochastic fluctuations.
binary-state dynamics are prevalent in nature, from societal dynamics to dynamical systems in physics. Reconstructing a network structure behind interacting binary-state dynamical systems is essential, as it can facil...
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binary-state dynamics are prevalent in nature, from societal dynamics to dynamical systems in physics. Reconstructing a network structure behind interacting binary-state dynamical systems is essential, as it can facilitate understanding of these dynamical systems and improve the accuracy of predicting dynamical behavior. So far, few works have focused on correlation information in binary-state temporal data to help reconstruct networks. In this study, we propose temporal correlation-based neural relational inference for binarydynamics (TCNRI), inspired by the maximum likelihood estimation of activation events in binarydynamics processes. TCNRI constructs instantaneous correlation features and long-term correlation features by analyzing activation events in the time series data. These features capture the correlation information and help TCNRI reconstruct the network structure. We treat the binary-state dynamical process as a Markov process and use neural networks to reproduce node dynamics based on the reconstructed network structure. We conduct simulations on the classic susceptible-infected-susceptible (SIS) dynamics and Ising dynamics. The results show that TCNRI significantly outperforms baseline models and can accurately reconstruct the network structure for both typical synthetic networks and real networks.
Inferring the structures and the dynamics of the complex networked systems based on time series data is a challenging problem. The existing reconstruction methods often rely on the knowledge of the dynamics on network...
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Inferring the structures and the dynamics of the complex networked systems based on time series data is a challenging problem. The existing reconstruction methods often rely on the knowledge of the dynamics on networks. In many cases, a prior knowledge of the dynamics is unknown, so it is natural to ask: is it possible to reconstruct network and estimate the dynamical processes on complex networks only rely on the observed data? In this article, we develop a framework to reconstruct the structures of networks with binary-state dynamics, in which the knowledge of the original dynamical processes is unknown. Within the reconstruction framework, the transition probabilities of binary dynamical processes are described by the Sigmoid function in logistic regression, we then apply the mean-field approximation to enable maximum likelihood estimation (MLE), which gives rise to that the network structure can be inferred by solving the linear system of equations. Meanwhile, the original dynamical processes can be simulated by estimating the parameters in the Sigmoid function. Our framework has been validated by a variety of binary dynamical processes on synthetic and empirical networks, indicating that our method can not only reveal the network structures but also estimate the dynamical processes. Moreover, the high accuracy of our method is highlighted by comparing it with the existing methods.
Complex networks with binary-state dynamics represent many meaningful behaviors in a variety of contexts. Reconstruction of networked systems hosting delayed binary processes with hidden nodes becomes an outstanding c...
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Complex networks with binary-state dynamics represent many meaningful behaviors in a variety of contexts. Reconstruction of networked systems hosting delayed binary processes with hidden nodes becomes an outstanding challenge in this field. To address this issue, we extend the statistical inference method to complex networked systems with distinct binary-state dynamics in presence of time delay and missing data. By exploiting the expectation-maximization (EM) algorithm, we implement the statistical inference based approach to different (i.e., random, small world, and scale-free) networks hosting delayed-binary processes. Our framework is completely data driven, and does not require any a prior knowledge about the detailed dynamical process on the network;especially, our method can independently infer each physical connectivity and estimate the time delay solely from the data of a pair of nodes in this link. We provide a physical understanding of the underlying mechanism;and extensive numerical simulations validate the robustness, efficiency, and accuracy of our method.
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