distanceprojection
Distance projection, also called metric projection or nearest-point projection, is the problem of finding, for a given point x in a metric space (X, d) and a nonempty subset A ⊆ X, the point(s) a ∈ A that are closest to x. The distance from x to A is dist(x, A) = inf_{a∈A} d(x, a).
In general, the projection set P_A(x) = { a ∈ A : d(x, a) = dist(x, A) } may be empty if
Examples include projection onto a linear subspace, which yields the orthogonal projection; projection onto a closed
Computation in finite-dimensional Euclidean space is often explicit: the projection onto a hyperplane with normal n
Applications of distance projections appear in approximation, optimization, signal processing, computer graphics, and machine learning, where
See also: metric projection; nearest point; best approximation.