AbsoluteCorrelation
AbsoluteCorrelation[v1,v2]
gives the absolute correlation between the vectors v1 and v2.
gives the absolute correlation matrix for the matrix m.
AbsoluteCorrelation[m1,m2]
gives the absolute correlation matrix for the matrices m1 and m2.
AbsoluteCorrelation[dist]
gives the absolute correlation matrix for the multivariate symbolic distribution dist.
AbsoluteCorrelation[dist,i,j]
gives the (i,j) absolute correlation for the multivariate symbolic distribution dist.
Details

- AbsoluteCorrelation[v1,v2] gives the unbiased estimate of the absolute correlation between v1 and v2.
- The lists v1 and v2 must be the same length.
- AbsoluteCorrelation[v1,v2] is equivalent to v1. Conjugate[v2]/Length[v1].
- For a matrix m with
columns, AbsoluteCorrelation[m] is a
×
matrix of the absolute correlations between columns of m.
- For an
×
matrix m1 and an
×
matrix m2, AbsoluteCorrelation[m1,m2] is a
×
matrix of the absolute correlations between columns of m1 and columns of m2.
- AbsoluteCorrelation[dist,i,j] gives Expectation[xixj,{x1,x2,…}∈dist].
- AbsoluteCorrelation[dist] gives an absolute correlation matrix with the (i,j)
entry given by AbsoluteCorrelation[dist,i,j].
Examples
open allclose allBasic Examples (3)
Scope (10)
Data (6)
Exact input yields exact output:
Approximate input yields approximate output:
Absolute correlation between vectors of complexes:
SparseArray data can be used:
Applications (3)
Compute the absolute correlation of two financial time series:
AbsoluteCorrelation can be used to measure linear association:
AbsoluteCorrelation can only detect monotonic relationships:
HoeffdingD can be used to detect a variety of dependence structures:
Properties & Relations (8)
The absolute correlation matrix is symmetric and positive semidefinite:
Covariance and AbsoluteCorrelation are the same for a distribution with zero mean:
Correlation and AbsoluteCorrelation agree for zero mean and unit marginal variances:
AbsoluteCorrelationFunction is the off-diagonal entry in the absolute correlation matrix:
AbsoluteCorrelationFunction for a list can be calculated using absolute correlation:
Calculate absolute correlation function for the data:
The absolute correlation tends to be large only on the diagonal of a random matrix:
The absolute correlation of a list with itself is proportional to the second moment:
The diagonal of an absolute correlation matrix is the second moment:
Text
Wolfram Research (2012), AbsoluteCorrelation, Wolfram Language function, https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html.
CMS
Wolfram Language. 2012. "AbsoluteCorrelation." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html.
APA
Wolfram Language. (2012). AbsoluteCorrelation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html