  We present the first classification of SOT/SP circular polarization
measurements with the aim of highlighting exhaustively the whole variety of
Stokes V shapes emerging from the quiet Sun. k-means is used to classify HINODE
SOT/SP Stokes V profiles observed in the quiet Sun network and internetwork
(IN). We analyze a 302 x 162 square arcsec field-of-view (FOV) which can be
considered a complete sample of quiet Sun measurements performed at at the disk
center with 0.32 arcsec angular resolution and 0.001 polarimetric sensitivity.
Such a classification allows us to divide the whole dataset in classes, with
each class represented by a cluster profile, i.e., the average of the profiles
in the class. The set of 35 cluster profiles derived from the analysis
completely characterizes SOT/SP quiet Sun measurements. The separation between
network and IN profile shapes is evident - classes in the network are not
present in the IN, and vice versa. Asymmetric profiles are approximatively 93 %
of the total number of profiles. Among these, approximatively 34 % of the
profiles are strongly asymmetric profiles, and they can be divided in three
families: blue-lobe, red-lobe, and Q-like profiles. The blue-lobe profiles tend
to be associated with upflows (granules), whereas the red-lobe and Q-like ones
appear in downflows (intergranular lanes). Such profiles need to be interpreted
considering model atmospheres different from a uniformly magnetized
Milne-Eddington (ME) atmosphere, i.e., characterized by gradients and/or
discontinuities in the magnetic field and velocity along the line-of-sight
(LOS).
