Identifying galaxy groups at high redshift from incomplete spectroscopic
  data: I. The group finder and application to zCOSMOS
  Identifying galaxy groups from redshift surveys of galaxies plays an
important role in connecting galaxies with the underlying dark matter
distribution. Current and future high-$z$ spectroscopic surveys, usually
incomplete in redshift sampling, present both opportunities and challenges to
identifying groups in the high-$z$ Universe. We develop a group finder that is
based on incomplete redshift samples combined with photometric data, using a
machine learning method to assign halo masses to identified groups. Test using
realistic mock catalogs shows that $\gtrsim 90\%$ of true groups with halo
masses $\rm M_h \gtrsim 10^{12} M_{\odot}/h$ are successfully identified, and
that the fraction of contaminants is smaller than $10\%$. The standard
deviation in the halo mass estimation is smaller than 0.25 dex at all masses.
We apply our group finder to zCOSMOS-bright and describe basic properties of
the group catalog obtained.
