  We identify multi-wavelength counterparts to 1,147 submillimeter sources from
the S2COSMOS SCUBA-2 survey of the COSMOS field by employing a recently
developed radio$+$machine-learning method trained on a large sample of
ALMA-identified submillimeter galaxies (SMGs), including 260 SMGs identified in
the AS2COSMOS pilot survey. In total, we identify 1,222
optical/near-infrared(NIR)/radio counterparts to the 897 S2COSMOS submillimeter
sources with S$_{850}$>1.6mJy, yielding an overall identification rate of
($78\pm9$)%. We find that ($22\pm5$)% of S2COSMOS sources have multiple
identified counterparts. We estimate that roughly 27% of these multiple
counterparts within the same SCUBA-2 error circles very likely arise from
physically associated galaxies rather than line-of-sight projections by chance.
The photometric redshift of our radio$+$machine-learning identified SMGs ranges
from z=0.2 to 5.7 and peaks at $z=2.3\pm0.1$. The AGN fraction of our sample is
($19\pm4$)%, which is consistent with that of ALMA SMGs in the literature.
Comparing with radio/NIR-detected field galaxy population in the COSMOS field,
our radio+machine-learning identified counterparts of SMGs have the highest
star-formation rates and stellar masses. These characteristics suggest that our
identified counterparts of S2COSMOS sources are a representative sample of SMGs
at z<3. We employ our machine-learning technique to the whole COSMOS field and
identified 6,877 potential SMGs, most of which are expected to have
submillimeter emission fainter than the confusion limit of our S2COSMOS surveys
(S$_{850}$<1.5mJy). We study the clustering properties of SMGs based on this
statistically large sample, finding that they reside in high-mass dark matter
halos ($(1.2\pm0.3)\times10^{13}\,h^{-1}\,\rm M_{\odot}$), which suggests that
SMGs may be the progenitors of massive ellipticals we see in the local
Universe.
