  We apply unsupervised machine learning techniques, mainly principal component
analysis (PCA), to compare and contrast the phase behavior and phase
transitions in several classical spin models - the square and
triangular-lattice Ising models, the Blume-Capel model, a highly degenerate
biquadratic-exchange spin-one Ising (BSI) model, and the 2D XY model, and
examine critically what machine learning is teaching us. We find that
quantified principal components from PCA not only allow exploration of
different phases and symmetry-breaking, but can distinguish phase transition
types and locate critical points. We show that the corresponding weight vectors
have a clear physical interpretation, which is particularly interesting in the
frustrated models such as the triangular antiferromagnet, where they can point
to incipient orders. Unlike the other well-studied models, the properties of
the BSI model are less well known. Using both PCA and conventional Monte Carlo
analysis, we demonstrate that the BSI model shows an absence of phase
transition and macroscopic ground-state degeneracy. The failure to capture the
`charge' correlations (vorticity) in the BSI model (XY model) from raw spin
configurations points to some of the limitations of PCA. Finally, we employ a
nonlinear unsupervised machine learning procedure, the `antoencoder method',
and demonstrate that it too can be trained to capture phase transitions and
critical points.
