  We use a dimension reduction algorithm, Uniform Manifold Approximation and
Projection (UMAP), to study dynamical structures inside a dark matter halo. We
use a zoom-in simulation of a Milky Way mass dark matter halo, and apply UMAP
on the 6 dimensional phase space in the dark matter field at z = 0. We find
that particles in the field are mapped to distinct clusters in the lower
dimensional space in a way that is closely related to their accretion history.
The largest cluster in UMAP space does not contain the entire mass of the Milky
Way virial region and neatly separates the older halo from the recently
accreted matter. Particles within this cluster, which only comprise $\sim 70\%$
of the Milky Way particles, have had several pericenter passages and are,
therefore, likely to be phase mixed, becoming dynamically uniform. The infall
region and recently accreted particle and substructure, even up to splashback,
form distinct components in the lower dimensional space; additionally, higher
angular momentum particles also take longer times to mix. Our work shows that
the current state of the Milky Way halo retains historical information,
particularly about the recent accretion history, and even a relatively old
structure is not dynamically uniform. We also explore UMAP as a pre-processing
step to find coherent subhalos in dark matter simulations.
