Learning the Structure of Connection Graphs

• URL: http://arxiv.org/abs/2510.11245v1
• Date: Mon, 13 Oct 2025 10:33:31 GMT
• Title: Learning the Structure of Connection Graphs
• Authors: Leonardo Di Nino, Gabriele D'Acunto, Sergio Barbarossa, Paolo Di Lorenzo,
• Abstract summary: Connection graphs (CGs) extend traditional graph models by coupling network topology with transformations, enabling the representation of global geometric consistency.<n>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 Laplacian.<n>We introduce the Structured Connection Graph Learning (SCGL) algorithm, a block-optimization procedure that jointly infers network topology, edge weights, and geometric structure.
• Score: 13.687470962704744
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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