Fast nonparametric classification based on data depth - Tatjana Lange; Karl Mosler; Pavlo Mozharovskyi (University of Cologne, Seminar of Economic and Social Statistics, 2012)
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.
Keywords: 330; Alpha-procedure; zonoid depth; DD-plot; pattern recognition; supervised learning; misclassification rate; Clusteranalyse; Nichtparametrisches Verfahren; Theorie