IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v32y2017i3d10.1007_s00180-016-0702-2.html
   My bibliography  Save this article

Estimation of level set trees using adaptive partitions

Author

Listed:
  • Lasse Holmström

    (University of Oulu)

  • Kyösti Karttunen

    (University of Oulu)

  • Jussi Klemelä

Abstract

We present methods for the estimation of level sets, a level set tree, and a volume function of a multivariate density function. The methods are such that the computation is feasible and estimation is statistically efficient in moderate dimensional cases ( $$d\approx 8$$ d ≈ 8 ) and for moderate sample sizes ( $$n\approx $$ n ≈ 50,000). We apply kernel estimation together with an adaptive partition of the sample space. We illustrate how level set trees can be applied in cluster analysis and in flow cytometry.

Suggested Citation

  • Lasse Holmström & Kyösti Karttunen & Jussi Klemelä, 2017. "Estimation of level set trees using adaptive partitions," Computational Statistics, Springer, vol. 32(3), pages 1139-1163, September.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-016-0702-2
    DOI: 10.1007/s00180-016-0702-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-016-0702-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-016-0702-2?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. Baíllo, Amparo & Cuesta-Albertos, Juan A. & Cuevas, Antonio, 2001. "Convergence rates in nonparametric estimation of level sets," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 27-35, May.
    2. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2001. "Cluster analysis: a further approach based on density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 36(4), pages 441-459, June.
    3. Cadre, BenoI^t, 2006. "Kernel estimation of density level sets," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 999-1023, April.
    4. Burman, Prabir & Polonik, Wolfgang, 2009. "Multivariate mode hunting: Data analytic tools with measures of significance," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1198-1218, July.
    5. Nolan, D., 1991. "The excess-mass ellipsoid," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 348-371, November.
    6. Duong, Tarn & Cowling, Arianna & Koch, Inge & Wand, M.P., 2008. "Feature significance for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4225-4242, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vuollo, Ville & Holmström, Lasse, 2018. "A scale space approach for exploring structure in spherical data," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 57-69.

    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. Christopher R. Genovese & Marco Perone-Pacifico & Isabella Verdinelli & Larry Wasserman, 2016. "Non-parametric inference for density modes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 99-126, January.
    2. José E. Chacón, 2020. "The Modal Age of Statistics," International Statistical Review, International Statistical Institute, vol. 88(1), pages 122-141, April.
    3. Cadre, BenoI^t, 2006. "Kernel estimation of density level sets," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 999-1023, April.
    4. José E. Chacón, 2019. "Mixture model modal clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(2), pages 379-404, June.
    5. Konstantin Eckle & Nicolai Bissantz & Holger Dette & Katharina Proksch & Sabrina Einecke, 2018. "Multiscale inference for a multivariate density with applications to X-ray astronomy," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 647-689, June.
    6. Elena Di Bernardino & Thomas Laloë & Véronique Maume-Deschamps & Clémentine Prieur, 2013. "Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory," Post-Print hal-00580624, HAL.
    7. Pedro Delicado & Philippe Vieu, 2017. "Choosing the most relevant level sets for depicting a sample of densities," Computational Statistics, Springer, vol. 32(3), pages 1083-1113, September.
    8. Alessandro Casa & Giovanna Menardi, 2022. "Nonparametric semi-supervised classification with application to signal detection in high energy physics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 531-550, September.
    9. Berthet, Philippe & Einmahl, John, 2020. "Cube Root Weak Convergence of Empirical Estimators of a Density Level Set," Other publications TiSEM 69103be2-c944-4ca1-b9e1-2, Tilburg University, School of Economics and Management.
    10. Mammen, Enno & Polonik, Wolfgang, 2013. "Confidence regions for level sets," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 202-214.
    11. Giovanna Menardi, 2016. "A Review on Modal Clustering," International Statistical Review, International Statistical Institute, vol. 84(3), pages 413-433, December.
    12. Delicado, Pedro & Vieu, Philippe, 2015. "Optimal level sets for bivariate density representation," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 1-18.
    13. Dau, Hai Dang & Laloë, Thomas & Servien, Rémi, 2020. "Exact asymptotic limit for kernel estimation of regression level sets," Statistics & Probability Letters, Elsevier, vol. 161(C).
    14. Leying Guan & Robert Tibshirani, 2022. "Prediction and outlier detection in classification problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 524-546, April.
    15. Di, J. & Kolaczyk, E., 2010. "Complexity-penalized estimation of minimum volume sets for dependent data," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1910-1926, October.
    16. Henderson, Daniel J. & Parmeter, Christopher F., 2012. "Normal reference bandwidths for the general order, multivariate kernel density derivative estimator," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2198-2205.
    17. Paula Saavedra-Nieves & Rosa M. Crujeiras, 2022. "Nonparametric estimation of directional highest density regions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(3), pages 761-796, September.
    18. Chiwoo Park & Jianhua Z. Huang & Yu Ding, 2010. "A Computable Plug-In Estimator of Minimum Volume Sets for Novelty Detection," Operations Research, INFORMS, vol. 58(5), pages 1469-1480, October.
    19. Yen-Chi Chen, 2017. "Modal Regression using Kernel Density Estimation: a Review," Papers 1710.07004, arXiv.org, revised Dec 2017.
    20. Federico Ferraccioli & Giovanna Menardi, 2023. "Modal clustering of matrix-variate data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 323-345, June.

    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:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-016-0702-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.