  We study the formation, evolution and collapse of dense cores by tracking
structures in a magnetohydrodynamic simulation of a star-forming cloud. We
identify cores using the dendrogram algorithm and utilize machine learning
techniques, including Neural Gas prototype learning and Fuzzy $c$-means
clustering, to analyze the density and velocity dispersion profiles of cores
together with six bulk properties. We produce a 2-d visualization using a
Uniform Manifold Approximation and Projection (UMAP), which facilitates the
connection between physical properties and three partially-overlapping phases:
i) unbound turbulent structures (Phase I), ii) coherent cores that have low
turbulence (Phase II), and iii) bound cores, many of which become protostellar
(Phase III). Within Phase II we identify a population of long-lived coherent
cores that reach a quasi-equilibrium state. Most prestellar cores form in Phase
II and become protostellar after evolving into Phase III. Due to the turbulent
cloud environment, the initial core properties do not uniquely predict the
eventual evolution, i.e., core evolution is stochastic, and cores follow no one
evolutionary path. The phase lifetimes are 1.0$\pm$0.1$\times$10$^5$ yr,
1.3$\pm$0.2$\times$10$^5$ yr, and 1.8$\pm$0.3$\times$10$^5$ yr for Phase I, II,
and III, respectively. We compare our results to NH$_3$ observations of dense
cores. Known coherent cores predominantly map into Phase II, while most
turbulent pressure-confined cores map to Phase I or III. We predict that a
significant fraction of observed starless cores have unresolved coherent
regions and that $\gtrsim 20$% of observed starless cores will not form stars.
Measurements of core radial profiles, in addition to the usual bulk properties,
will enable more accurate predictions of core evolution.
