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 Half-space may refer to:
* Half-space (geometry), either of the two parts into which a plane divides Euclidean space
* Half-space (punctuation), a spacing character half the width of a regular space
* (Poincaré) Half-space model, a model of 3-di ...
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) In statistics and computational geometry, the notion of centerpoint is a generalization of the median to data in higher-dimensional Euclidean space. Given a set of points in ''d''-dimensional space, a centerpoint of the set is a point such that ...
Computational geometry
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