Similarly, it is possible to update the Cholesky factor when a row or column is added, without creating the inverse of the correlation matrix explicitly.
22.
However, mean-centering is unnecessary in any regression analysis, as one uses a correlation matrix and the data are already centered after calculating correlations.
23.
One strategy is to define a correlation matrix " A " which is then multiplied by a scalar to give a covariance matrix : this must be positive definite.
24.
For this reason, some of the methods used in the analyses of the correlation matrix ( e . g . the PCA ) have to be replaced or are less efficient.
25.
Since this soft-thresholding procedure applied to a pairwise correlation matrix leads to weighted adjacency matrix, the ensuing analysis is referred to as weighted gene co-expression network analysis.
26.
"' Image factoring "'is based on the correlation matrix of predicted variables rather than actual variables, where each variable is predicted from the others using multiple regression.
27.
Where K is as above and \ bar r the mean of the K ( K-1 ) / 2 non-redundant upper triangular, or lower triangular, correlation matrix ).
28.
The estimation of MVAR coefficients is based on calculation of the correlation matrix " R ij " of " k " signals " X i " from multivariate set.
29.
Equivalently, the correlation matrix can be seen as the covariance matrix of the standardized random variables X _ i / \ sigma ( X _ i ) for i = 1, \ dots, n.
30.
In terms of the correlation matrix, this corresponds with focusing on explaining the off-diagonal terms ( i . e . shared co-variance ), while PCA focuses on explaining the terms that sit on the diagonal.
