29: Intrinsic Dimension of Undirected Networks on Unknown Latent Manifold of Constant Curvature

Music City Center 

This study proposes a novel data-driven approach for estimating the intrinsic dimension and curvature of complex networks by modeling them as simply connected, complete Riemannian manifolds of constant curvature. Unlike existing methods that rely on predefined structural assumptions, our framework integrates the k-nearest neighbors (KNN) algorithm with the TWO-NN approach, enabling adaptive and robust network partitioning, which enhances the accuracy of dimensionality reduction while preserving essential geometric properties. By leveraging fundamental forms and hypothesis testing, our method ensures precise curvature estimation and manifold classification. Experimental results demonstrate superior robustness against noise and improved effectiveness in capturing intrinsic network geometry, significantly advancing the interpretability and applicability of network data analysis.

Intrinsic dimension estimation

Manifold geometry

Simply connected Riemannian manifold 

Section on Statistical Computing