# Reconstructing propagation networks with natural diversity and identifying hidden sources

@article{Shen2014ReconstructingPN, title={Reconstructing propagation networks with natural diversity and identifying hidden sources}, author={Zhesi Shen and Wen-Xu Wang and Ying Fan and Zengru Di and Ying-Cheng Lai}, journal={Nature Communications}, year={2014}, volume={5} }

Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic dynamical processes from limited time series remains to be an outstanding problem. Here we develop a framework based on compressed sensing to reconstruct complex networks on which stochastic spreading dynamics take place. We apply the methodology to a large…

## 160 Citations

### Network reconstruction from infection cascades

- Computer ScienceJournal of the Royal Society Interface
- 2019

It is shown that it is possible to reconstruct the whole structure of an interaction network and to simultaneously infer the complete time course of activation spreading, relying just on single epoch (i.e. snapshot) or time-scattered observations of a small number of activity cascades.

### Universal data-based method for reconstructing complex networks with binary-state dynamics.

- Computer SciencePhysical review. E
- 2017

This work develops a universal data-based linearization approach that is applicable to systems with linear, nonlinear, discontinuous, or stochastic dynamics governed by monotonic functions and represents a general paradigm for reconstructing, understanding, and exploiting complex networked systems with binary-state dynamics.

### Reconstructing signed networks via Ising dynamics.

- Computer ScienceChaos
- 2018

This work develops a statistical inference approach to fully reconstruct the signed network structure (positive links, negative links, and nonexistent links) based on the Ising dynamics and shows that the approach can transfer the problem of maximum likelihood estimation into the problems of solving linear systems of equations.

### Fundamental limitations of network reconstruction

- Computer ScienceArXiv
- 2015

It is found that reconstructing any property of the interaction Matrix is generically as difficult as reconstructing the interaction matrix itself, requiring equally informative temporal data.

### Statistical inference approach to structural reconstruction of complex networks from binary time series.

- Computer SciencePhysical review. E
- 2018

This work develops a method to ascertain the neighbors of any node in the network based solely on binary data, thereby recovering the full topology of the network and contributing an additional piece to the rapidly expanding "toolbox" of data based reverse engineering of complex networked systems.

### Inferring network properties based on the epidemic prevalence

- Computer Science, MathematicsAppl. Netw. Sci.
- 2019

It is found that some of the network metrics, namely those that are sensitive to the epidemic prevalence, can be roughly inferred if the network type is known, and a simulated annealing link-rewiring algorithm is proposed to obtain an optimized network whose prevalence is close to the benchmark.

### Data based reconstruction of complex multiplex networks

- Computer Science
- 2018

This work articulate a mean-field based maximum likelihood estimation framework and demonstrates the power of the reconstruction framework and characterize its performance using binary time series from a class of prototypical duplex network systems that host two distinct types of spreading dynamics.

### Inferring Network Structure and Estimating Dynamical Process From Binary-State Data via Logistic Regression

- Computer Science, MathematicsIEEE Transactions on Systems, Man, and Cybernetics: Systems
- 2021

This article develops a framework to reconstruct the structures of networks with binary-state dynamics, in which the knowledge of the original dynamical processes is unknown, and applies 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.

### A two-stage reconstruction method for complex networked system with hidden nodes.

- Computer ScienceChaos
- 2022

This work has developed a robust two-stage network reconstruction method for complex networks with hidden nodes from a small amount of observed time series data that takes full advantage of the natural sparsity of complex networks and the potential symmetry constraints in dynamic interactions.

### Robust Reconstruction of Continuously Time-Varying Topologies of Weighted Networks

- MathematicsIEEE Transactions on Circuits and Systems I: Regular Papers
- 2018

A new way to reconstruct the structures of continuously time-varying and state-dependent networks by reconstructing the Taylor expansion coefficients of couplings by integrating each component’s information of a high-dimensional node is developed.

## References

SHOWING 1-10 OF 74 REFERENCES

### Network Reconstruction Based on Evolutionary-Game Data via Compressive Sensing

- Computer SciencePhysical Review X
- 2011

Based on compressive sensing, an efficient approach to reconstructing complex networks under game-based interactions from small amounts of data is developed, demonstrating that the extremely challenging problem of reverse engineering of complex networks can be addressed even when the underlying dynamical processes are governed by realistic, evolutionary-game type of interactions in discrete time.

### Time-series–based prediction of complex oscillator networks via compressive sensing

- Computer Science
- 2011

This work demonstrates that the network-reconstruction problem can be casted into the form X=G·a, where the vector X and matrix G are determined by the time series and a is a sparse vector to be estimated that contains all nonzero power series coefficients in the mathematical functions of all existing couplings among the nodes.

### Detecting hidden nodes in complex networks from time series.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

The paradigm for detecting hidden nodes is expected to find applications in a variety of fields where identifying hidden or black-boxed objects based on a limited amount of data is of interest.

### Hierarchical structure and the prediction of missing links in networks

- Computer ScienceNature
- 2008

This work presents a general technique for inferring hierarchical structure from network data and shows that the existence of hierarchy can simultaneously explain and quantitatively reproduce many commonly observed topological properties of networks.

### On the Convexity of Latent Social Network Inference

- Computer ScienceNIPS
- 2010

This work considers contagions propagating over the edges of an unobserved social network, and presents a maximum likelihood approach based on convex programming with a l1-like penalty term that encourages sparsity to identify the optimal network that best explains the observed data.

### Multiscale, resurgent epidemics in a hierarchical metapopulation model.

- EconomicsProceedings of the National Academy of Sciences of the United States of America
- 2005

This work introduces a class of metapopulation models in which homogeneous mixing holds within local contexts, and that these contexts are embedded in a nested hierarchy of successively larger domains and allow diseases to spread stochastically.

### Thresholds for epidemic spreading in networks

- MathematicsPhysical review letters
- 2010

It is conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.

### Revealing network connectivity from response dynamics.

- MathematicsPhysical review letters
- 2007

This work considers networks of coupled phase oscillators and explicitly study their long-term stationary response to temporally constant driving, finding good predictions of the actual connectivity even for formally underdetermined problems.

### Statistical mechanics of complex networks

- Computer ScienceArXiv
- 2001

A simple model based on these two principles was able to reproduce the power-law degree distribution of real networks, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.

### Noise bridges dynamical correlation and topology in coupled oscillator networks.

- PhysicsPhysical review letters
- 2010

Noise leads to a general, one-to-one correspondence between the dynamical correlation and the connections among oscillators for a variety of node dynamics and network structures, enabling an accurate prediction of the full network topology based solely on measuring the dynamicals correlation.