NormalizedSquaredEuclideanDistance
NormalizedSquaredEuclideanDistance[u,v]
gives the normalized squared Euclidean distance between vectors u and v.
Examples
open all close allBasic Examples (2)
Scope (2)
Compute the distance between any vectors of equal length:
NormalizedSquaredEuclideanDistance[RandomReal[5, 100], RandomReal[5, 100]]Compute the distance between vectors of any precision:
NormalizedSquaredEuclideanDistance[N[{1, 5, 2, 3, 10}, 50], N[{4, 15, 20, 5, 5}, 50]]Applications (1)
Properties & Relations (2)
Normalized squared Euclidean distance includes a squared Euclidean distance scaled by norms:
u = {a, b, c};
v = {x, y, z};
1 / 2 * Norm[(u - Mean@u) - (v - Mean@v)] ^ 2 / (Norm[u - Mean@u] ^ 2 + Norm[v - Mean@v] ^ 2)NormalizedSquaredEuclideanDistance[u, v] == %The normalized squared Euclidean distance of two vectors or real numbers is in the range from 0 to 1:
u = {a, b, c};
v = {x, y, z};
First@Maximize[N@NormalizedSquaredEuclideanDistance[u, v], {a, b, c, x, y, z}, Reals]First@Minimize[N@NormalizedSquaredEuclideanDistance[u, v], {a, b, c, x, y, z}, Reals]Text
Wolfram Research (2010), NormalizedSquaredEuclideanDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/NormalizedSquaredEuclideanDistance.html.
CMS
Wolfram Language. 2010. "NormalizedSquaredEuclideanDistance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NormalizedSquaredEuclideanDistance.html.
APA
Wolfram Language. (2010). NormalizedSquaredEuclideanDistance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NormalizedSquaredEuclideanDistance.html