# Robust Reconstruction of Complex Networks from Sparse Data

arXiv: https://arxiv.org/abs/1501.04731 · HTML: https://mlsanity.com/paper/1501.04731/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2015.

## Built on by (most cited first, 6 of 6)

- [Structural Inference of Networked Dynamical Systems with Universal Differential Equations](https://mlsanity.com/paper/2207.04962/) (2022)
- [Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structures](https://mlsanity.com/paper/2311.00902/) (2023)
- [Versatile Reservoir Computing for Heterogeneous Complex Networks](https://mlsanity.com/paper/2505.15219/) (2025)
- [Tomography of time-dependent quantum spin networks with machine learning](https://mlsanity.com/paper/2103.08645/) (2021)
- [Machine learning of network inference enhancement from noisy measurements](https://mlsanity.com/paper/2309.02050/) (2023)
- [Parallel Network Reconstruction with Multi-directional Regularization](https://mlsanity.com/paper/2411.11464/) (2024)

## Abstract (arXiv)

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.