  Wide-field photometric surveys enable searches of rare yet interesting
objects, such as strongly lensed quasars or quasars with a bright host galaxy.
Past searches for lensed quasars based on their optical and near infrared
properties have relied on photometric cuts and spectroscopic pre-selection (as
in the Sloan Quasar Lens Search), or neural networks applied to photometric
samples. These methods rely on cuts in morphology and colours, with the risk of
losing many interesting objects due to scatter in their population properties,
restrictive training sets, systematic uncertainties in catalog-based
magnitudes, and survey-to-survey photometric variations. Here, we explore the
performance of a Gaussian Mixture Model to separate point-like quasars, quasars
with an extended host, and strongly lensed quasars using griz psf and model
magnitudes and WISE W1, W2. The choice of optical magnitudes is due to their
presence in all current and upcoming releases of wide-field surveys, whereas UV
information is not always available. We then assess the contamination from blue
galaxies and the role of additional features such as W3 magnitudes or psf-model
terms as morphological information. As a demonstration, we conduct a search in
a random 10% of the SDSS footprint, and we provide the catalog of the 43 SDSS
object with the highest `lens' score in our selection that survive visual
inspection, and are spectroscopically confirmed to host active nuclei. We
inspect archival data and find images of 5/43 objects in the Hubble Legacy
Archive, including 2 known lenses. The code and materials are available to
facilitate follow-up.
