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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Applications (stat.AP) |
| Cite as: | arXiv:2510.15141 [stat.ML] |
| (or arXiv:2510.15141v4 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2510.15141 arXiv-issued DOI via DataCite |
Submission history
From: Zelong Bi [view email]
[v1]
Thu, 16 Oct 2025 20:59:46 UTC (1,165 KB)
[v2]
Mon, 27 Oct 2025 23:02:56 UTC (1,167 KB)
[v3]
Sat, 1 Nov 2025 00:45:20 UTC (1,168 KB)
[v4]
Thu, 14 May 2026 09:32:37 UTC (1,071 KB)