  In this work we apply the principal component analysis (PCA) method with
kernel trick to study classification of phases and phase transition in
classical XY models in frustrated lattices. Comparing to our previous work with
linear PCA method, the kernel PCA can capture non-linear function. In this
case, the Z2 chiral order of classical spins in these lattices are indeed a
non-linear function of the input spin configurations. In addition to the
principal component revealed by linear PCA, the kernel PCA can find out two
more principal components using data generated by Monte Carlo simulation at
various temperatures at input. One of them relates to the strength of the U(1)
order parameter and the other directly manifests the chiral order parameter
that characterizes the Z2 symmetry breaking. For a temperature resolved study,
the temperature dependence of the principal eigenvalue associated with the Z2
symmetry breaking clearly shows a second order phase transition behavior.
