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In this work we apply the principal component analysis (PCA) method withkernel trick to study classification of phases and phase transition inclassical XY models in frustrated lattices. Comparing to our previous work withlinear PCA method, the kernel PCA can capture non-linear function. In thiscase, the Z2 chiral order of classical spins in these lattices are indeed anon-linear function of the input spin configurations. In addition to theprincipal component revealed by linear PCA, the kernel PCA can find out twomore principal components using data generated by Monte Carlo simulation atvarious temperatures at input. One of them relates to the strength of the U(1)order parameter and the other directly manifests the chiral order parameterthat characterizes the Z2 symmetry breaking. For a temperature resolved study,the temperature dependence of the principal eigenvalue associated with the Z2symmetry breaking clearly shows a second order phase transition behavior.

Machine Learning of Frustrated Classical Spin Models. II. Kernel Principal Component Analysis