CorrelationDistance
CorrelationDistance[u,v]
gives the correlation coefficient distance between vectors u and v.
Examples
open all close allBasic Examples (2)
Scope (2)
Applications (1)
Properties & Relations (3)
Correlation distance includes a dot product scaled by norms:
u = {a, b, c};
v = {x, y, z};1 - (u - Mean[u]).(v - Mean[v]) / (Norm[u - Mean[u]]Norm[v - Mean[v]])CorrelationDistance[u, v] == %Correlation distance includes a dot product scaled by Euclidean distances from the mean:
u = {a, b, c};
v = {x, y, z};scale = (EuclideanDistance[u, Mean[u]]EuclideanDistance[v, Mean[v]])CorrelationDistance[u, v] == 1 - (u - Mean[u]).(v - Mean[v]) / scaleCorrelationDistance is equivalent to CosineDistance of vectors shifted by their means:
u = {a, b, c};
v = {x, y, z};CorrelationDistance[u, v] == CosineDistance[u - Mean[u], v - Mean[v]]Text
Wolfram Research (2007), CorrelationDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/CorrelationDistance.html.
CMS
Wolfram Language. 2007. "CorrelationDistance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CorrelationDistance.html.
APA
Wolfram Language. (2007). CorrelationDistance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CorrelationDistance.html