# State-Space Network Topology Identification from Partial Observations

## TL;DR

This paper presents a novel method for recovering network topology from partial observations using extended subspace techniques, bridging control theory and graph signal processing with theoretical guarantees and an convergent algorithm.

## Contribution

It introduces a unified approach combining system identification and graph signal processing to recover network structure with provable guarantees from partial data.

## Key findings

- Algorithm successfully recovers network topology from partial observations.
- Theoretical guarantees ensure accurate topology identification under certain conditions.
- Numerical results validate the effectiveness and applicability of the proposed method.

## Abstract

In this work, we explore the state-space formulation of a network process to recover, from partial observations, the underlying network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system identification literature and extend them to the network topology identification problem. This approach provides a unified view of the traditional network control theory and signal processing on graphs. In addition, it provides theoretical guarantees for the recovery of the topological structure of a deterministic continuous-time linear dynamical system from input-output observations even though the input and state interaction networks might be different. The derived mathematical analysis is accompanied by an algorithm for identifying, from data, a network topology consistent with the dynamics of the system and conforms to the prior information about the underlying structure. The proposed algorithm relies on alternating projections and is provably convergent. Numerical results corroborate the theoretical findings and the applicability of the proposed algorithm.