The paucity of hypervelocity stars (HVSs) known to date has severely hampered their potential to investigate the stellar population of the Galactic Centre and the Galactic Potential. The first Gaia data release gives an opportunity to increase the current sample. The challenge is the disparity between the expected number of hypervelocity stars and that of bound background stars. We have applied a novel data mining algorithm based on machine learning techniques, an artificial neural network, to the Tycho-Gaia astrometric solution (TGAS) catalogue. With no pre-selection of data, we could exclude immediately $sim 99 %$ of the stars in the catalogue and find 80 candidates with more than $90%$ predicted probability to be HVSs, based only on their position, proper motions, and parallax. We have cross-checked our findings with other spectroscopic surveys, determining radial velocities for 30 and spectroscopic distances for 5 candidates. In addition, follow-up observations have been carried out at the Isaac Newton Telescope for 22 stars, for which we obtained radial velocities and distance estimates. We discover 14 stars with a total velocity in the Galactic rest frame > 400 km/s, and 5 of these have a probability $>50%$ of being unbound from the Milky Way. Tracing back their orbits in different Galactic potential models we find one possible unbound HVS with velocity $sim$ 520 km/s, 5 bound HVSs, and, notably, 5 runaway stars with median velocity between 400 and 780 km/s. At the moment, uncertainties in the distance estimates and ages are too large to confirm the nature of our candidates by narrowing down their ejection location, and we wait for future Gaia releases to validate the quality of our sample. This test successfully demonstrates the feasibility of our new data mining routine.
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