We analyze an extremely deep 450- \micron 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 \micron 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- \micron 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 SMG candidates with similar colors .
The number density , radio and/or mid-infrared detection rates , redshift and stellar mass distributions , and the stacked 450- \micron 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- \micron SMG candidate sample , we measure the two-point autocorrelation functions from z = 3 down to z = 0.5 .
We find that the SMG candidates reside in halos with masses of \simeq ( 2.0 \pm 0.5 ) \times 10 ^ { 13 } h ^ { -1 } M _ { \sun } across this redshift range .
We do not find evidence of downsizing that has been suggested by other recent observational studies .