2025/10/16 by Zelong Bi, Zhuanfang Bi, Pierre Lafaye de Micheaux +2
Computer Science · Mathematics · #Face and Expression Recognition #Morphological variations and asymmetry #Topological and Geometric Data Analysis #cs.LG #stat.AP #stat.ML
paper · pdf · doi:10.48550/arxiv.2510.15141
openalex publication_date 2025/10/16 · openalex created_date 2025/10/21 · openalex updated_date 2026/07/28
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.