SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES) IV: Spatial clustering
  and halo masses of 450-$\mu$m-selected sub-millimeter galaxies
  We analyze an extremely deep 450-$\mu$m image
($1\sigma=0.56$\,mJy\,beam$^{-1}$) of a $\simeq 300$\,arcmin$^{2}$ area in the
CANDELS/COSMOS field as part of the SCUBA-2 Ultra Deep Imaging EAO Survey
(STUDIES). We select a robust (signal-to-noise ratio $\geqslant 4$) and
flux-limited ($\geqslant 4$\,mJy) sample of 164 sub-millimeter galaxies (SMGs)
at 450-$\mu$m that have $K$-band counterparts in the COSMOS2015 catalog
identified from radio or mid-infrared imaging. Utilizing this SMG sample and
the 4705 $K$-band-selected non-SMGs that reside within the noise level
$\leqslant 1$\,mJy\,beam$^{-1}$ region of the 450-$\mu$m image as a training
set, we develop a machine-learning classifier using $K$-band magnitude and
color-color pairs based on the thirteen-band photometry available in this
field. We apply the trained machine-learning classifier to the wider COSMOS
field (1.6\,deg$^{2}$) using the same COSMOS2015 catalog and identify a sample
of 6182 450-$\mu$m SMG candidates with similar colors. The number density,
radio and/or mid-infrared detection rates, redshift and stellar mass
distributions, and the stacked 450-$\mu$m fluxes of these SMG candidates, from
the S2COSMOS observations of the wide field, agree with the measurements made
in the much smaller CANDELS field, supporting the effectiveness of the
classifier. Using this 450-$\mu$m SMG candidate sample, we measure the
two-point autocorrelation functions from $z=3$ down to $z=0.5$. We find that
the 450-$\mu$m SMG candidates reside in halos with masses of $\simeq
(2.0\pm0.5) \times10^{13}\,h^{-1}\,\rm M_{\odot}$ across this redshift range.
We do not find evidence of downsizing that has been suggested by other recent
observational studies.
