  Thompson's partition of a cyclic subnormal operator into normal and
completely non-normal components is combined with a non-commutative calculus
for hyponormal operators for separating outliers from the cloud, in rather
general point distributions in the plane. The main result provides exact
transformation formulas from the power moments of the prescribed point
distribution into the moments of the uniform mass carried by the cloud. The
proposed algorithm solely depends on the Hessenberg matrix associated to the
original data. The robustness of the algorithm is reflected by the
insensitivity of the output under trace class, or by a theorem of Voiculescu,
under certain Hilbert-Schmidt class, additive perturbations of the Hessenberg
matrix.
