Manifold Dimension Estimation via Local Graph Structure

ArXi:2510.15141v4 Announce Type: replace-cross Most existing manifold dimension estimators rely on the assumption that the underlying manifold is locally flat within the neighborhoods under consideration. recently, curvature-adjusted principal component analysis (CA-PCA) has emerged as a powerful alternative by explicitly accounting for the manifold's curvature. Motivated by these ideas, we propose a manifold dimension estimation framework that captures the local graph structure of the manifold through regression on local PCA coordinates. Within this framework, we.