Identifying galaxies, quasars and stars with machine learning: a new catalogue of classifications for 111 million SDSS sources without spectra

We use 2.4\,million spectroscopically labelled sources from the SDSS catalogue to train an optimized random forest classifier using photometry from the Sloan Digital Sky Survey (SDSS) and Widefield Infrared Survey Explorer (WISE). We apply this machine learning model to 111 million previously unlabelled sources from the SDSS photometric catalogue without existing spectroscopic observations. Our new catalogue contains 49.7 million galaxies, 2.4 million quasars, and 59.2 million stars. We provide individual classification probabilities for each source, with 6.4 million galaxies (13\%), 0.35 million quasars (14\%) and 44.3 million stars (75\%) having classification probabilities greater than 0.99, and 34.8 million galaxies (70\%), 0.77 million quasars (32\%) and 55.3 million stars (93\%) having classification probabilities greater than 0.9. We determine Precision, Recall and F$_1$ score as a function of feature selection, including scenarios with additional external variables. 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 use 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 using the 2.4\,million spectroscopically labelled training sources. We confirm that when the same algorithm is applied to the 111 million sources without spectra it is in strong agreement with the class labels applied by our random forest model.