Computing halfspace depth contours based on the idea of a circular sequence

This paper presents a new efficient algorithm for exactly computing the halfspace depth contours based on the idea of a circular sequence. Unlike the existing methods, the proposed algorithm segments the unit sphere directly relying on the permutations that correspond to the projections of observations onto some unit directions, without having to use the technique of parametric programming. Some data examples are also provided to illustrate the performance of the proposed algorithm.