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Fast nonparametric classification based on data depth

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  • Tatjana Lange
  • Karl Mosler
  • Pavlo Mozharovskyi

Abstract

A new procedure, called D D α-procedure, is developed to solve the problem of classifying d-dimensional objects into q ≥ 2 classes. The procedure is nonparametric; it uses q-dimensional depth plots and a very efficient algorithm for discrimination analysis in the depth space [0,1] q . Specifically, the depth is the zonoid depth, and the algorithm is the α-procedure. In case of more than two classes several binary classifications are performed and a majority rule is applied. Special treatments are discussed for ‘outsiders’, that is, data having zero depth vector. The D Dα-classifier is applied to simulated as well as real data, and the results are compared with those of similar procedures that have been recently proposed. In most cases the new procedure has comparable error rates, but is much faster than other classification approaches, including the support vector machine. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Tatjana Lange & Karl Mosler & Pavlo Mozharovskyi, 2014. "Fast nonparametric classification based on data depth," Statistical Papers, Springer, vol. 55(1), pages 49-69, February.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:1:p:49-69
    DOI: 10.1007/s00362-012-0488-4
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    References listed on IDEAS

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    Cited by:

    1. Xiaohui Liu & Shihua Luo & Yijun Zuo, 2020. "Some results on the computing of Tukey’s halfspace median," Statistical Papers, Springer, vol. 61(1), pages 303-316, February.
    2. Wang, Jin, 2019. "Asymptotics of generalized depth-based spread processes and applications," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 363-380.
    3. Daniel Hlubinka & Irène Gijbels & Marek Omelka & Stanislav Nagy, 2015. "Integrated data depth for smooth functions and its application in supervised classification," Computational Statistics, Springer, vol. 30(4), pages 1011-1031, December.
    4. Olusola Samuel Makinde, 2019. "Classification rules based on distribution functions of functional depth," Statistical Papers, Springer, vol. 60(3), pages 629-640, June.
    5. Stanislav Nagy, 2021. "Halfspace depth does not characterize probability distributions," Statistical Papers, Springer, vol. 62(3), pages 1135-1139, June.
    6. Christophe Denis & Charlotte Dion & Miguel Martinez, 2020. "Consistent procedures for multiclass classification of discrete diffusion paths," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 516-554, June.
    7. Xinyu Zhou & Wei Wu, 2024. "Statistical Depth in Spatial Point Process," Mathematics, MDPI, vol. 12(4), pages 1-20, February.
    8. Massimo Aria & Antonio D’Ambrosio & Carmela Iorio & Roberta Siciliano & Valentina Cozza, 2020. "Dynamic recursive tree-based partitioning for malignant melanoma identification in skin lesion dermoscopic images," Statistical Papers, Springer, vol. 61(4), pages 1645-1661, August.
    9. Kotík, Lukáš & Hlubinka, Daniel, 2017. "A weighted localization of halfspace depth and its properties," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 53-69.
    10. Giovanni Saraceno & Claudio Agostinelli, 2021. "Robust multivariate estimation based on statistical depth filters," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 935-959, December.
    11. Wei Shao & Yijun Zuo, 2020. "Computing the halfspace depth with multiple try algorithm and simulated annealing algorithm," Computational Statistics, Springer, vol. 35(1), pages 203-226, March.
    12. Vencalek, Ondrej & Pokotylo, Oleksii, 2018. "Depth-weighted Bayes classification," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 1-12.
    13. Dyckerhoff, Rainer & Mozharovskyi, Pavlo, 2016. "Exact computation of the halfspace depth," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 19-30.
    14. Ye Dong & Stephen Lee, 2014. "Depth functions as measures of representativeness," Statistical Papers, Springer, vol. 55(4), pages 1079-1105, November.
    15. J. A. Cuesta-Albertos & M. Febrero-Bande & M. Oviedo de la Fuente, 2017. "The $$\hbox {DD}^G$$ DD G -classifier in the functional setting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 119-142, March.
    16. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2017. "Multivariate and functional classification using depth and distance," 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. 11(3), pages 445-466, September.
    17. Oleksii Pokotylo & Karl Mosler, 2019. "Classification with the pot–pot plot," Statistical Papers, Springer, vol. 60(3), pages 903-931, June.
    18. Liu, Xiaohui & Rahman, Jafer & Luo, Shihua, 2019. "Generalized and robustified empirical depths for multivariate data," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 70-79.

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