{"ID":2854890,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.15141","arxiv_id":"2510.15141","title":"Manifold Dimension Estimation via Local Graph Structure","abstract":"Most existing manifold dimension estimators rely on the assumption that the underlying manifold is locally flat within the neighborhoods under consideration. More 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 introduce two representative estimators: quadratic embedding (QE) and total least squares (TLS). Experiments on both synthetic and real-world datasets demonstrate that these methods perform competitively with, and often outperform, state-of-the-art approaches.","short_abstract":"Most existing manifold dimension estimators rely on the assumption that the underlying manifold is locally flat within the neighborhoods under consideration. More recently, curvature-adjusted principal component analysis (CA-PCA) has emerged as a powerful alternative by explicitly accounting for the manifold's curvatur...","url_abs":"https://arxiv.org/abs/2510.15141","url_pdf":"https://arxiv.org/pdf/2510.15141v4","authors":"[\"Zelong Bi\",\"Pierre Lafaye de Micheaux\"]","published":"2025-10-16T20:59:46Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"stat.AP\"]","methods":"[]","has_code":false}