  We used 3.1 million spectroscopically labelled sources from the Sloan Digital
Sky Survey (SDSS) to train an optimised random forest classifier using
photometry from the SDSS and the Widefield Infrared Survey Explorer (WISE). We
applied this machine learning model to 111 million previously unlabelled
sources from the SDSS photometric catalogue which did not have existing
spectroscopic observations. Our new catalogue contains 50.4 million galaxies,
2.1 million quasars, and 58.8 million stars. We provide individual
classification probabilities for each source, with 6.7 million galaxies (13%),
0.33 million quasars (15%), and 41.3 million stars (70%) having classification
probabilities greater than 0.99; and 35.1 million galaxies (70%), 0.72 million
quasars (34%), and 54.7 million stars (93%) having classification probabilities
greater than 0.9. Precision, Recall, and F1 score were determined as a function
of selected features and magnitude error. We investigate the effect of class
imbalance on our machine learning model and discuss the implications of
transfer learning for populations of sources at fainter magnitudes than the
training set. We used a non-linear dimension reduction technique, Uniform
Manifold Approximation and Projection (UMAP), in unsupervised, semi-supervised,
and fully-supervised schemes to visualise the separation of galaxies, quasars,
and stars in a two-dimensional space. When applying this algorithm to the 111
million sources without spectra, it is in strong agreement with the class
labels applied by our random forest model.
