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= Tukey Depth = |
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In [[computational geometry]], the notion of '''Tukey depth''' is a measure of the depth due to [[John Tukey]] of a point in fixed point set. Given a set of points $P$ in ''d''-dimensional space, a point ''p'' has Tukey depth ''k'' where ''k'' is the smallest number of points any closed [[halfspace]] that contains ''p'' has. |
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For example, for any point on the convex hull there is always a (closed) halfspace that contains only that point, and hence its Tukey depth is 1. |
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== Tukey mean and relation to centerpoint == |
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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''. |
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Revision as of 08:47, 9 March 2020
Tukey Depth
In computational geometry, the notion of Tukey depth is a measure of the depth due to John Tukey of a point in fixed point set. Given a set of points $P$ in d-dimensional space, a point p has Tukey depth k where k is the smallest number of points any closed halfspace that contains p has.
For example, for any point on 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).