Spectral clustering and model reduction for weakly-connected coherent network systems

TL;DR

This paper introduces a spectral clustering-based model reduction technique for large-scale dynamic networks, effectively capturing coherent groups and their interactions, with theoretical justification and validated through numerical experiments.

Contribution

It presents a novel model reduction method that identifies coherent groups via spectral clustering and constructs a reduced network representing group dynamics and interactions.

Findings

The method accurately identifies coherent groups in large networks.

The reduced model preserves essential dynamic behavior.

Numerical experiments validate the theoretical approach.

Abstract

We propose a novel 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. Our approach is theoretically justified under a random graph setting. Finally, numerical experiments align with and validate our theoretical findings.