Star-Galaxy Classification in Multi-Band Optical Imaging
  Ground-based optical surveys such as PanSTARRS, DES, and LSST, will produce large catalogs to limiting magnitudes of r > 24. Star-galaxy separation poses a major challenge to such surveys because galaxies---even very compact galaxies---outnumber halo stars at these depths. We investigate photometric classification techniques on stars and galaxies with intrinsic FWHM < 0.2 arcsec. We consider unsupervised spectral energy distribution template fitting and supervised, data-driven Support Vector Machines (SVM). For template fitting, we use a Maximum Likelihood (ML) method and a new Hierarchical Bayesian (HB) method, which learns the prior distribution of template probabilities from the data. SVM requires training data to classify unknown sources; ML and HB don't. We consider i.) a best-case scenario (SVM_best) where the training data is (unrealistically) a random sampling of the data in both signal-to-noise and demographics, and ii.) a more realistic scenario where training is done on higher signal-to-noise data (SVM_real) at brighter apparent magnitudes. Testing with COSMOS ugriz data we find that HB outperforms ML, delivering ~80% completeness, with purity of ~60-90% for both stars and galaxies, respectively. We find no algorithm delivers perfect performance, and that studies of metal-poor main-sequence turnoff stars may be challenged by poor star-galaxy separation. Using the Receiver Operating Characteristic curve, we find a best-to-worst ranking of SVM_best, HB, ML, and SVM_real. We conclude, therefore, that a well trained SVM will outperform template-fitting methods. However, a normally trained SVM performs worse. Thus, Hierarchical Bayesian template fitting may prove to be the optimal classification method in future surveys. 
Ross Fadely, David W. Hogg, and Beth Willman
astro-ph.IM astro-ph.CO astro-ph.GA