从观测信号中学习连接图的拓扑与几何结构，提升建模精度。
Learning the Structure of Connection Graphs
- 基于一致性假设的伪似然最大化的结构化学习框架
- 在拓扑恢复和几何保真度上优于现有方法，计算高效
- 适合需要精确建模网络几何关系的研究者
连接图（CG）通过将网络拓扑与正交变换耦合，实现全局几何一致性表示，在同步、黎曼信号处理和神经层流扩散等任务中发挥关键作用。本文解决从观测信号直接学习连接图的逆问题，提出一种基于一致性假设的最大伪似然框架，该框架通过谱性质将连接拉普拉斯算子与组合拉普拉斯算子关联。基于此，我们引入结构化连接图学习（SCGL）算法，一种在黎曼流形上的块优化过程，可联合推断网络拓扑、边权重与几何结构。实验表明，SCGL在拓扑恢复与几何保真度上持续优于现有基线方法，且计算效率高。
原文摘要 · Abstract (English)
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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