Local angles and dimension estimation from data on manifolds

Mateo Díaz, Adolfo J. Quiroz, Mauricio Velasco

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

7 Citas (Scopus)

Resumen

For data living in a manifold M⊆R m and a point p∈M, we consider a statistic U k,n which estimates the variance of the angle between pairs (X i −p,X j −p) of vectors, for data points X i , X j , 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 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 and real datasets.

Idioma originalInglés
Páginas (desde-hasta)229-247
Número de páginas19
PublicaciónJournal of Multivariate Analysis
Volumen173
DOI
EstadoPublicada - set. 2019
Publicado de forma externa

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