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The success of algorithms in the analysis of high-dimensional data is oftenattributed to the manifold hypothesis, which supposes that this data lie on ornear a manifold of much lower dimension. It is often useful to determine orestimate the dimension of this manifold before performing dimension reduction,for instance. Existing methods for dimension estimation are calibrated using aflat unit ball. In this paper, we develop CA-PCA, a version of local PCA basedinstead on a calibration of a quadratic embedding, acknowledging the curvatureof the underlying manifold. Numerous careful experiments show that thisadaptation improves the estimator in a wide range of settings.

CA-PCA: Manifold Dimension Estimation, Adapted for Curvature