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Fast nonparametric classification based on data depth

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  • Lange, Tatjana
  • Mosler, Karl
  • Mozharovskyi, Pavlo

Abstract

A new procedure, called DD-procedure, is developed to solve the problem of classifying d-dimensional objects into q Ï 2 classes. The procedure is completely 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 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 DD-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 SVM.

Suggested Citation

  • Lange, Tatjana & Mosler, Karl & Mozharovskyi, Pavlo, 2012. "Fast nonparametric classification based on data depth," Discussion Papers in Econometrics and Statistics 1/12, University of Cologne, Institute of Econometrics and Statistics.
  • Handle: RePEc:zbw:ucdpse:112
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    References listed on IDEAS

    as
    1. Christmann, Andreas & Rousseeuw, Peter J., 2001. "Measuring overlap in binary regression," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 65-75, July.
    2. K. Mosler, 2003. "Central regions and dependency," Econometrics 0309004, EconWPA.
    3. Subhajit Dutta & Anil Ghosh, 2012. "On robust classification using projection depth," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 657-676, June.
    4. Jörnsten, Rebecka, 2004. "Clustering and classification based on the L1 data depth," Journal of Multivariate Analysis, Elsevier, vol. 90(1), pages 67-89, July.
    5. Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The random Tukey depth," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4979-4988, July.
    6. Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, March.
    7. Anil K. Ghosh & Probal Chaudhuri, 2005. "On Maximum Depth and Related Classifiers," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 327-350.
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    Citations

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    Cited by:

    1. Ye Dong & Stephen Lee, 2014. "Depth functions as measures of representativeness," Statistical Papers, Springer, vol. 55(4), pages 1079-1105, November.
    2. 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.
    3. 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.
    4. repec:spr:advdac:v:11:y:2017:i:3:d:10.1007_s11634-016-0269-3 is not listed on IDEAS
    5. Zhaoyuan Li & Jianfeng Yao, 2016. "On two simple and effective procedures for high dimensional classification of general populations," Statistical Papers, Springer, vol. 57(2), pages 381-405, April.
    6. Dyckerhoff, Rainer & Mozharovskyi, Pavlo, 2016. "Exact computation of the halfspace depth," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 19-30.
    7. repec:eee:jmvana:v:157:y:2017:i:c:p:53-69 is not listed on IDEAS

    More about this item

    Keywords

    Alpha-procedure; zonoid depth; DD-plot; pattern recognition; supervised learning; misclassification rate;

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