  We present GHOST, a database of 16,175 spectroscopically classified
supernovae and the properties of their host galaxies. We have developed a host
galaxy association method using image gradients that achieves fewer
misassociations for low-z hosts and higher completeness for high-z hosts than
previous methods. We use dimensionality reduction to identify the host galaxy
properties that distinguish supernova classes. Our results suggest that the
hosts of SLSNe, SNe Ia, and core collapse supernovae can be separated using
host brightness information and extendedness measures derived from the host's
light profile. Next, we train a random forest model with data from GHOST to
predict supernova class using exclusively host galaxy information and the
radial offset of the supernova. We can distinguish SNe Ia and core collapse
supernovae with ~70% accuracy without any photometric data from the event
itself. Vera C. Rubin Observatory will usher in a new era of transient
population studies, demanding improved photometric tools for rapid
identification and classification of transient events. By identifying the host
features with high discriminatory power, we will maintain SN sample purities
and continue to identify scientifically relevant events as data volumes
increase. The GHOST database and our corresponding software for associating
transients with host galaxies are both publicly available.
