CA-PCA: Manifold Dimension Estimation, Adapted for Curvature
Abstract
The success of algorithms in the analysis of high-dimensional data is often attributed to the manifold hypothesis, which supposes that this data lie on or near a manifold of much lower dimension. It is often useful to determine or estimate the dimension of this manifold before performing dimension reduction, for instance. Existing methods for dimension estimation are calibrated using a flat unit ball. In this paper, we develop CA-PCA, a version of local PCA based instead on a calibration of a quadratic embedding, acknowledging the curvature of the underlying manifold. Numerous careful experiments show that this adaptation improves the estimator in a wide range of settings.
Keywords
Cite
@article{arxiv.2309.13478,
title = {CA-PCA: Manifold Dimension Estimation, Adapted for Curvature},
author = {Anna C. Gilbert and Kevin O'Neill},
journal= {arXiv preprint arXiv:2309.13478},
year = {2024}
}
Comments
Updates to calculations and text after small error found in computation of constant used in main algorithm. Experiments rerun, conclusions remain the same. Some new experiments also added