Description Usage Arguments Details Value Author(s) References See Also Examples
View source: R/mModeCovariance.R
Estimates the m-mode covariance matrix from an array of array-valued observations.
1 | mModeCovariance(x, m, center = TRUE, normalize = TRUE)
|
x |
Array of order higher than two with the last dimension corresponding to the sampling units. |
m |
The mode with respect to which the covariance matrix is to be computed. |
center |
Logical, indicating whether the observations should be centered prior to computing the covariance matrix. Default is |
normalize |
Logical, indicating whether the resulting matrix is divided by |
The m-mode covariance matrix provides a higher order analogy for the ordinary covariance matrix of a random vector and is computed for a random tensor X of size p_1 x p_2 x ... x p_r as Cov_m(X) = E(X(m) X(m)^T)/(p_1 ... p_(m-1) p_(m+1) ... p_r), where X(m) is the centered m-flattening of X. The algorithm computes the estimate of this based on the sample x
.
The m
-mode covariance matrix of x
having the size p_m x p_m.
Joni Virta
Virta, J., Li, B., Nordhausen, K. and Oja, H., (2017), Independent component analysis for tensor-valued data, Journal of Multivariate Analysis, doi: 10.1016/j.jmva.2017.09.008
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