Anna Bartkowiak, Krystyna Zietak, 
"Backprojection of data vectors using a given covariance matrix"

Very often analyzed data are contamined with outliers
which are due to some erroneous recording. After sorting out the suspected
erroneous observations and coming to the conclusion that they are really
erroneous, we would like to adjust them to the proper values.

In the paper we propose two methods (called Plug-in and Procrustes) which
- taking into account the interdependencies  between the variables
provided in a robust covariance matrix S - permit to reconstruct
the data  matrix  in such a way, that its covariance matrix is exactly
equal to the given robust covariance matrix S. We call this process 
backprojection through the robust covariance matrix. The proposed  method
of backprojection is shown on four benchmark data sets.

Keywords: outliers, robust covariance matrix, 
visualization of multivariate data