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We analyze an extremely deep 450-$\mu$m image($1\sigma=0.56$\,mJy\,beam$^{-1}$) of a $\simeq 300$\,arcmin$^{2}$ area in theCANDELS/COSMOS field as part of the SCUBA-2 Ultra Deep Imaging EAO Survey(STUDIES). We select a robust (signal-to-noise ratio $\geqslant 4$) andflux-limited ($\geqslant 4$\,mJy) sample of 164 sub-millimeter galaxies (SMGs)at 450-$\mu$m that have $K$-band counterparts in the COSMOS2015 catalogidentified from radio or mid-infrared imaging. Utilizing this SMG sample andthe 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 trainingset, we develop a machine-learning classifier using $K$-band magnitude andcolor-color pairs based on the thirteen-band photometry available in thisfield. We apply the trained machine-learning classifier to the wider COSMOSfield (1.6\,deg$^{2}$) using the same COSMOS2015 catalog and identify a sampleof 6182 450-$\mu$m SMG candidates with similar colors. The number density,radio and/or mid-infrared detection rates, redshift and stellar massdistributions, and the stacked 450-$\mu$m fluxes of these SMG candidates, fromthe S2COSMOS observations of the wide field, agree with the measurements madein the much smaller CANDELS field, supporting the effectiveness of theclassifier. Using this 450-$\mu$m SMG candidate sample, we measure thetwo-point autocorrelation functions from $z=3$ down to $z=0.5$. We find thatthe 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 recentobservational studies.

SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES) IV: Spatial clustering and halo masses of 450-$\mu$m-selected sub-millimeter galaxies