Web: http://arxiv.org/abs/2110.06357

Sept. 16, 2022, 1:12 a.m. | Uzu Lim, Harald Oberhauser, Vidit Nanda

cs.LG updates on arXiv.org arxiv.org

Consider a set of points sampled independently near a smooth compact
submanifold of Euclidean space. We provide mathematically rigorous bounds on
the number of sample points required to estimate both the dimension and the
tangent spaces of that manifold with high confidence. The algorithm for this
estimation is Local PCA, a local version of principal component analysis. Our
results accommodate for noisy non-uniform data distribution with the noise that
may vary across the manifold, and allow simultaneous estimation at multiple …

arxiv math space

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