  Galaxies host a wide array of internal stellar components, which need to be
decomposed accurately in order to understand their formation and evolution.
While significant progress has been made with recent integral-field
spectroscopic surveys of nearby galaxies, much can be learned from analyzing
the large sets of realistic galaxies now available through state-of-the-art
hydrodynamical cosmological simulations. We present an unsupervised machine
learning algorithm, named auto-GMM, based on Gaussian mixture models, to
isolate intrinsic structures in simulated galaxies based on their kinematic
phase space. For each galaxy, the number of Gaussian components allowed by the
data is determined through a modified Bayesian information criterion. We test
our method by applying it to prototype galaxies selected from the cosmological
simulation IllustrisTNG. Our method can effectively decompose most galactic
structures. The intrinsic structures of simulated galaxies can be inferred
statistically by non-human supervised identification of galaxy structures. We
successfully identify four kinds of intrinsic structures: cold disks, warm
disks, bulges, and halos. Our method fails for barred galaxies because of the
complex kinematics of particles moving on bar orbits.
