The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback--Leibler distance to measure the performance of filtering algorithms in recovering the underlying correlation matrix when the variables are described by a multivariate Gaussian distribution. Here we use the Kullback--Leibler distance to investigate the performance of filtering methods based on Random Matrix Theory and on the shrinkage technique. We also present some results on the application of the Kullback--Leibler distance to multivariate data which are non Gaussian distributed.

PACS numbers: 02.50.Sk, 05.45.Tp, 05.40.Ca, 02.10.Yn