On the Optimality of the Max-Depth and Max-Rank Classifiers for Spherical Data

The main goal of supervised learning is to construct a function from labeled training data which assigns arbitrary new data points to one of the labels. Classification tasks may be solved by using some measures of data point centrality with respect to the labeled groups considered. Such a measure of centrality is called data depth. In this paper, we investigate conditions under which depth-based classifiers for directional data are optimal. We show that such classifiers are equivalent to the Bayes (optimal) classifier when the considered distributions are rotationally symmetric, unimodal, differ only in location and have equal priors. The necessity of such assumptions is also discussed.