In
computational geometry, the Tukey depth is a measure of the depth of a point in a fixed set of points. The concept is named after its inventor,
John Tukey. Given a set of points
in ''d''-dimensional space, a point ''p'' has Tukey depth ''k'' where ''k'' is the smallest number of points in any closed
halfspace that contains ''p''.
For example, for any extreme point of the
convex hull there is always a (closed) halfspace that contains only that point, and hence its Tukey depth is 1.
Tukey mean and relation to centerpoint
A centerpoint ''c'' of a point set of size ''n'' is nothing else but a point of Tukey depth of at least ''n''/(''d'' + 1).
See also
*
Centerpoint (geometry)
Computational geometry
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