# Topology Identification under Spatially Correlated Noise

arXiv: https://arxiv.org/abs/2012.04175 · HTML: https://mlsanity.com/paper/2012.04175/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise](https://mlsanity.com/paper/2312.05974/) (2023)
- [Network Topology Inference from Smooth Signals Under Partial Observability](https://mlsanity.com/paper/2410.05707/) (2024)
- [A scalable multi-step least squares method for network identification with unknown disturbance topology](https://mlsanity.com/paper/2106.07548/) (2021)
- [Inferring the Graph of Networked Dynamical Systems under Partial Observability and Spatially Colored Noise](https://mlsanity.com/paper/2312.11324/) (2023)

## Abstract (arXiv)

This article addresses the problem of reconstructing the topology of a network of agents interacting via linear dynamics, while being excited by exogenous stochastic sources that are possibly correlated across the agents, from time-series measurements alone. It is shown, under the assumption that the correlations are affine in nature, such network of nodal interactions is equivalent to a network with added agents, represented by nodes that are latent, where no corresponding time-series measurements are available; however, here all exogenous excitements are spatially (that is, across agents) uncorrelated. Generalizing affine correlations, it is shown that, under polynomial correlations, the latent nodes in the expanded networks can be excited by clusters of noise sources, where the clusters are uncorrelated with each other. The clusters can be replaced with a single noise source if the latent nodes are allowed to have non-linear interactions. Finally, using the sparse plus low-rank matrix decomposition of the imaginary part of the inverse power spectral density matrix (IPSDM) of the time-series data, the topology of the network is reconstructed. Under non conservative assumptions, the correlation graph is retrieved.