A Survey and Comparative Evaluation of Intrinsic Dimension Estimators under the Manifold Hypothesis

ArXi:2509.15517v2 Announce Type: replace The manifold hypothesis suggests that high-dimensional data often lie on or near a low-dimensional manifold. Estimating the dimension of this manifold is essential for leveraging its structure, yet existing work on dimension estimation is fragmented and lacks systematic evaluation. This article provides a comprehensive survey for both researchers and practitioners. We review often-overlooked theoretical foundations and present eight representative estimators.