Learning the Structure of Connection Graphs
This work addresses a problem in fields like synchronization and neural sheaf diffusion, offering a novel method for learning CGs, though it is incremental as it builds on existing graph models.
The paper tackles the inverse problem of learning connection graphs (CGs) from observed signals, proposing the SCGL algorithm, which outperforms baselines in topological recovery and geometric fidelity while being computationally efficient.
Connection graphs (CGs) extend traditional graph models by coupling network topology with orthogonal transformations, enabling the representation of global geometric consistency. They play a key role in applications such as synchronization, Riemannian signal processing, and neural sheaf diffusion. In this work, we address the inverse problem of learning CGs directly from observed signals. We propose a principled framework based on maximum pseudo-likelihood under a consistency assumption, which enforces spectral properties linking the connection Laplacian to the underlying combinatorial Laplacian. Based on this formulation, we introduce the Structured Connection Graph Learning (SCGL) algorithm, a block-optimization procedure over Riemannian manifolds that jointly infers network topology, edge weights, and geometric structure. Our experiments show that SCGL consistently outperforms existing baselines in both topological recovery and geometric fidelity, while remaining computationally efficient.