  A new procedure, called DDa-procedure, is developed to solve the problem of
classifying d-dimensional objects into q >= 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
alpha-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 DDa-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.
