Ray-Shooting Depth: Computing Statistical Data Depth of Point Sets in the Plane
نویسندگان
چکیده
Over the past several decades, many combinatorial measures have been devised for capturing the statistical data depth of a set of n points in R. These include Tukey depth [15], Oja depth [12], Simplicial depth [10] and several others. Recently Fox et al. [7] have defined the Ray-Shooting depth of a point set, and given a topological proof for the existence of points with high Ray-Shooting depth in R. In this paper, we present an O(nlogn)-time algorithm for computing a point of high RayShooting depth. We also present a linear time approximation algorithm.
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