Regular Article

Statistical Papers

, Volume 55, Issue 1, pp 49-69

First online:

Fast nonparametric classification based on data depth

  • Tatjana LangeAffiliated withHochschule Merseburg, Geusaer Straße
  • , Karl MoslerAffiliated withUniversität zu Köln, Albertus-Magnus-Platz Email author 
  • , Pavlo MozharovskyiAffiliated withUniversität zu Köln, Albertus-Magnus-Platz

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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.


Alpha-procedure Zonoid depth DD-plot Pattern recognition Supervised learning Misclassification rate Support vector machine