# Learning Coherent Clusters in Weakly-Connected Network Systems

arXiv: https://arxiv.org/abs/2211.15301 · HTML: https://mlsanity.com/paper/2211.15301/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 28 Nov 2022.

## Builds on (most cited first, 8 of 8)

- [Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embedding](https://mlsanity.com/paper/1310.0532/) (2013)
- [Hypergraph Spectral Clustering in the Weighted Stochastic Block Model](https://mlsanity.com/paper/1805.08956/) (2018)
- [Dynamic Droop Control in Low-inertia Power Systems](https://mlsanity.com/paper/1908.10983/) (2019)
- [Dynamics Concentration of Large-Scale Tightly-Connected Networks](https://mlsanity.com/paper/1903.06017/) (2019)
- [Coherence and Concentration in Tightly-Connected Networks](https://mlsanity.com/paper/2101.00981/) (2021)
- [Structure-preserving Model Reduction of Parametric Power Networks](https://mlsanity.com/paper/2102.05179/) (2021)
- [Long Wavelength Coherency in Well Connected Electric Power Networks](https://mlsanity.com/paper/2112.05048/) (2021)
- [Spectral clustering and model reduction for weakly-connected coherent network systems](https://mlsanity.com/paper/2209.13701/) (2022)

## Abstract (arXiv)

We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the network feedback. Then, a reduced network is built, where each node represents the aggregate dynamics of each coherent group, and the reduced network captures the dynamic coupling between the groups. We provide an upper bound on the approximation error when the network graph is randomly generated from a weight stochastic block model. Finally, numerical experiments align with and validate our theoretical findings.