  We present a classification of galaxies in the Pan-STARRS1 (PS1) 3$\pi$
survey based on their recent star formation history and morphology.
Specifically, we train and test two Random Forest (RF) classifiers using
photometric features (colors and moments) from the PS1 data release 2. Labels
for the morphological classification are taken from Huertas-Company+2011, while
labels for the star formation fraction (SFF) are from the Blanton+2005 catalog.
We find that colors provide more predictive accuracy than photometric moments.
We morphologically classify galaxies as either early- or late-type, and our RF
model achieves a 78\% classification accuracy. Our second model classifies
galaxies as having either a low-to-moderate or high SFF. This model achieves an
89\% classification accuracy. We apply both RF classifiers to the entire PS1
$3\pi$ dataset, allowing us to assign two scores to each PS1 source:
$P_\mathrm{HSFF}$, which quantifies the probability of having a high SFF, and
$P_\mathrm{spiral}$, which quantifies the probability of having a late-type
morphology. Finally, as a proof of concept, we apply our classification
framework to supernova (SN) host-galaxies from the Zwicky Transient Factory and
the Lick Observatory Supernova Search samples. We show that by selecting on
$P_\mathrm{HSFF}$ or $P_\mathrm{spiral}$ it is possible to significantly
enhance or suppress the fraction of core-collapse SNe (or thermonuclear SNe) in
the sample with respect to random guessing. This result demonstrates how
contextual information can aid transient classifications at the time of first
detection. In the current era of spectroscopically-starved time-domain
astronomy, prompt automated classification is paramount.
