Tukey depth

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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 ${\displaystyle P}$ 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)

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