  Nucleation phenomena commonly observed in our every day life are of
fundamental, technological and societal importance in many areas, but some of
their most intimate mechanisms remain however to be unraveled. Crystal
nucleation, the early stages where the liquid-to-solid transition occurs upon
undercooling, initiates at the atomic level on nanometer length and
sub-picoseconds time scales and involves complex multidimensional mechanisms
with local symmetry breaking that can hardly be observed experimentally in the
very details. To reveal their structural features in simulations without a
priori, an unsupervised learning approach founded on topological descriptors
loaned from persistent homology concepts is proposed. Applied here to a
monatomic metal, namely Tantalum (Ta), it shows that both translational and
orientational ordering always come into play simultaneously when homogeneous
nucleation starts in regions with low five-fold symmetry.
