Local angles and dimension estimation from data on manifolds

Mateo Díaz, Adolfo J. Quiroz and Mauricio Velasco

Journal of Multivariate Analysis, 2019, vol. 173, issue C, 229-247

Abstract: For data living in a manifold M⊆Rm and a point p∈M, we consider a statistic Uk,n which estimates the variance of the angle between pairs (Xi−p,Xj−p) of vectors, for data points Xi, Xj, near p, and we 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 Uk,n is found under minimal regularity assumptions. Performance of the proposed methodology is compared against state-of-the-art methods on simulated data and real datasets.

Keywords: Angle variance; Dimension estimation; Local U-statistics; Manifold learning (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.jmva.2019.02.014

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