Functional classification and the random Tukey depth : practical issues

Abstract

Depths are used to attempt to order the points of a multidimensional or infinite dimensional set from the “center of the set” to the “outer of it”. There are few definitions of depth which are valid in the functional case. One of them is the so-called random Tukey depth, which is based on some randomly chosen one-dimensional projections and thus varies (randomly) from computation to computation. Some theoretical properties of this depth are well-known, but it has not yet been studied from a practical point of view. The aim of this paper is to analyze its behavior in classification problems, the interest of this study being increased by the random character of the depth. To do this, we compare the performance of the random Tukey depth in a real data set with the results obtained with the López-Pintado and Romo depths.