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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. --

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Paper provided by University of Cologne, Department for Economic and Social Statistics in its series Discussion Papers in Statistics and Econometrics with number 1/12.

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Date of creation: 2012
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Handle: RePEc:zbw:ucdpse:112

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Related research

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

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