IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v173y2019icp229-247.html
   My bibliography  Save this article

Local angles and dimension estimation from data on manifolds

Author

Listed:
  • Díaz, Mateo
  • Quiroz, Adolfo J.
  • Velasco, Mauricio

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.

Suggested Citation

  • Díaz, Mateo & Quiroz, Adolfo J. & Velasco, Mauricio, 2019. "Local angles and dimension estimation from data on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 229-247.
    • Handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:229-247
    DOI: 10.1016/j.jmva.2019.02.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X18302446
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2019.02.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kaufmann, E. & Reiss, R. -D., 1992. "On conditional distributions of nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 67-76, July.
    2. Brito, M.R. & Quiroz, A.J. & Yukich, J.E., 2013. "Intrinsic dimension identification via graph-theoretic methods," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 263-277.
    3. Brito, María R. & Quiroz, Adolfo J. & Yukich, J. E., 2002. "Graph-Theoretic Procedures for Dimension Identification," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 67-84, April.
    4. Jonathan M. Borwein & Marc Chamberland, 2007. "Integer Powers of Arcsin," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-10, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. S. Camelo & M. González-Lima & A. Quiroz, 2015. "Nearest neighbors methods for support vector machines," Annals of Operations Research, Springer, vol. 235(1), pages 85-101, December.
    2. Bugni, Federico A. & Canay, Ivan A., 2021. "Testing continuity of a density via g-order statistics in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 221(1), pages 138-159.
    3. Wang, Ke & Nagaraja, H.N., 2010. "Distribution of extremal order statistics from large subsets of concomitants," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 534-539, April.
    4. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jos Mara, 2009. "Multivariate order statistics via multivariate concomitants," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 946-951, May.
    5. Ling Zhu, 2022. "A Natural Approximation to the Complete Elliptic Integral of the First Kind," Mathematics, MDPI, vol. 10(9), pages 1-8, April.
    6. Chunli Li & Wenchang Chu, 2024. "Generating Functions for Binomial Series Involving Harmonic-like Numbers," Mathematics, MDPI, vol. 12(17), pages 1-15, August.
    7. Brito, M.R. & Quiroz, A.J. & Yukich, J.E., 2013. "Intrinsic dimension identification via graph-theoretic methods," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 263-277.
    8. Ling Zhu, 2022. "The Natural Approaches of Shafer-Fink Inequality for Inverse Sine Function," Mathematics, MDPI, vol. 10(4), pages 1-8, February.
    9. González-Barrios, José María & Quiroz, Adolfo J., 2003. "A clustering procedure based on the comparison between the k nearest neighbors graph and the minimal spanning tree," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 23-34, March.
    10. Qinying He & H. Nagaraja & Chunjie Wu, 2013. "Efficient simulation of complete and censored samples from common bivariate exponential distributions," Computational Statistics, Springer, vol. 28(6), pages 2479-2494, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:229-247. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.