  We present a new clustering method, Significance Mode Analysis (SigMA), to
extract co-spatial and co-moving stellar populations from large-scale surveys
such as ESA Gaia. The method studies the topological properties of the density
field in the multidimensional phase space. We validate SigMA on simulated
clusters and find that it outperforms competing methods, especially in cases
where many clusters are closely spaced. We apply the new method to Gaia DR3
data of the closest OB association to Earth, Scorpio-Centaurus (Sco-Cen), and
find more than 13,000 co-moving young objects, with about 19% of these having a
sub-stellar mass. SigMA finds 37 co-moving clusters in Sco-Cen. These clusters
are independently validated by their narrow HRD sequences and, to a certain
extent, by their association with massive stars too bright for Gaia, hence
unknown to SigMA. We compare our results with similar recent work and find that
the SigMA algorithm recovers richer populations, is able to distinguish
clusters with velocity differences down to about 0.5 km s$^{-1}$, and reaches
cluster volume densities as low as 0.01 sources/pc$^3$. The 3D distribution of
these 37 coeval clusters implies a larger extent and volume for the Sco-Cen OB
association than typically assumed in the literature. Additionally, we find the
association to be more actively star-forming and dynamically more complex than
previously thought. We confirm that the star-forming molecular clouds in the
Sco-Cen region, namely, Ophiuchus, L134/L183, Pipe Nebula, Corona Australis,
Lupus, and Chamaeleon, are part of the Sco-Cen The application of SigMA to
Sco-Cen demonstrates that advanced machine learning tools applied to the superb
Gaia data allows to construct an accurate census of the young populations, to
quantify their dynamics, and to reconstruct the recent star formation history
of the local Milky Way.
