Papers › Local angles and dimension estimation from data on manifolds
Local angles and dimension estimation from data on manifolds
Mateo Díaz, Adolfo J. Quiroz, Mauricio Velasco
For data living in a manifold M⊆ℝᵐ and a point p∈M we consider a statistic U_(k,n) which estimates the variance of the angle between pairs of vectors Xᵢ-p and Xⱼ-p, for data points Xᵢ, Xⱼ, near p, and evaluate this statistic as a tool for estimation of the intrinsic dimension of M at p. Consistency of the local dimension estimator is established and the asymptotic distribution of U_(k,n) is found under minimal regularity assumptions. Performance of the proposed methodology is compared against state-of-the-art methods on simulated data.
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