  The graphical representation of the correlation matrix by means of different
multivariate statistical methods is reviewed, a comparison of the different
procedures is presented with the use of an example data set, and an improved
representation with better fit is proposed. Principal component analysis is
widely used for making pictures of correlation structure, though as shown a
weighted alternating least squares approach that avoids the fitting of the
diagonal of the correlation matrix outperforms both principal component
analysis and principal factor analysis in approximating a correlation matrix.
Weighted alternating least squares is a very strong competitor for principal
component analysis, in particular if the correlation matrix is the focus of the
study, because it improves the representation of the correlation matrix, often
at the expense of only a minor percentage of explained variance for the
original data matrix, if the latter is mapped onto the correlation biplot by
regression. In this article, we propose to combine weighted alternating least
squares with an additive adjustment of the correlation matrix, and this is seen
to lead to further improved approximation of the correlation matrix.
