# Identifiability of dynamical networks with partial node measurements

arXiv: https://arxiv.org/abs/1803.05885 · HTML: https://mlsanity.com/paper/1803.05885/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2018.

## Built on by (most cited first, 2 of 2)

- [Dealing with collinearity in large-scale linear system identification using Bayesian regularization](https://mlsanity.com/paper/2203.13633/) (2022)
- [Dealing with Collinearity in Large-Scale Linear System Identification Using Gaussian Regression](https://mlsanity.com/paper/2302.10959/) (2023)

## Abstract (arXiv)

Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear transfer functions and are excited by known external excitation signals and/or unknown noise signals. A major research question concerns the identifiability of the whole network - topology and all transfer functions - from the measured node signals and external excitation signals. So far all results on this topic have assumed that all node signals are measured. This paper presents the first results for the situation where not all node signals are measurable, under the assumptions that (1) the topology of the network is known, and (2) each node is excited by a known external excitation. Using graph theoretical properties, we show that the transfer functions that can be identified depend essentially on the topology of the paths linking the corresponding vertices to the measured nodes. A practical outcome is that, under those assumptions, a network can often be identified using only a small subset of node measurements.