  We establish an explicit data-driven criterion for identifying the
solid-liquid transition of two-dimensional self-propelled colloidal particles
in the far from equilibrium parameter regime, where the transition points
predicted by different conventional empirical criteria for melting and freezing
diverge. This is achieved by applying a hybrid machine learning approach that
combines unsupervised learning with supervised learning to analyze over one
million of system's configurations in the nonequilibrium parameter regime.
Furthermore, we establish a generic data-driven evaluation function, according
to which the performance of different empirical criteria can be systematically
evaluated and improved. In particular, by applying this evaluation function, we
identify a new nonequilibrium threshold value for the long-time diffusion
coefficient, based on which the predictions of the corresponding empirical
criterion are greatly improved in the far from equilibrium parameter regime.
These data-driven approaches provide a generic tool for investigating phase
transitions in complex systems where conventional empirical ones face
difficulties.
