Fast nonparametric classification based on data depth

TL;DR

This paper introduces the DDa-procedure, a fast, nonparametric classification method using data depth and the alpha-procedure, effective for multi-class problems and outperforming some existing methods in speed.

Contribution

The paper presents a novel nonparametric classification method based on data depth plots and an efficient algorithm, improving speed while maintaining accuracy.

Findings

Comparable error rates to existing methods

Significantly faster than SVM and similar classifiers

Effective for multi-class classification with special handling for outsiders

Abstract

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.