Quasar and galaxy classification in Gaia Data Release 2
  We construct a supervised classifier based on Gaussian Mixture Models to
probabilistically classify objects in Gaia data release 2 (GDR2) using only
photometric and astrometric data in that release. The model is trained
empirically to classify objects into three classes -- star, quasar, galaxy --
for G<=14.5 mag down to the Gaia magnitude limit of G=21.0 mag. Galaxies and
quasars are identified for the training set by a cross-match to objects with
spectroscopic classifications from the Sloan Digital Sky Survey. Stars are
defined directly from GDR2. When allowing for the expectation that quasars are
500 times rarer than stars, and galaxies 7500 times rarer than stars (the class
imbalance problem), samples classified with a threshold probability of 0.5 are
predicted to have purities of 0.43 for quasars and 0.28 for galaxies, and
completenesses of 0.58 and 0.72 respectively. The purities can be increased up
to 0.60 by adopting a higher threshold. Not accounting for this expected low
frequency of extragalactic objects (the class prior) would give both
erroneously optimistic performance predictions and severely impure samples.
Applying our model to all 1.20 billion objects in GDR2 with the required
features, we classify 2.3 million objects as quasars and 0.37 million objects
as galaxies (with individual probabilities above 0.5). The small number of
galaxies is due to the strong bias of the satellite detection algorithm and
on-ground data selection against extended objects. We infer the true number of
quasars and galaxies -- as these classes are defined by our training set -- to
be 690,000 and 110,000 respectively (+/- 50%). The aim of this work is to see
how well extragalactic objects can be classified using only GDR2 data. Better
classifications should be possible with the low resolution spectroscopy (BP/RP)
planned for GDR3.
