  An unconventional magnet may be mapped onto a simple ferromagnet by the
existence of a high-symmetry point. Knowledge of conventional ferromagnetic
systems may then be carried over to provide insight into more complex orders.
Here we demonstrate how an unsupervised and interpretable machine-learning
approach can be used to search for potential high-symmetry points in
unconventional magnets without any prior knowledge of the system. The method is
applied to the classical Heisenberg-Kitaev model on a honeycomb lattice, where
our machine learns the transformations that manifest its hidden $O(3)$
symmetry, without using data of these high-symmetry points. Moreover, we
clarify that, in contrast to the stripy and zigzag orders, a set of $D_2$ and
$D_{2h}$ ordering matrices provides a more complete description of the
magnetization in the Heisenberg-Kitaev model. In addition, our machine also
learns the local constraints at the phase boundaries, which manifest a
subdimensional symmetry. This paper highlights the importance of explicit order
parameters to many-body spin systems and the property of interpretability for
the physical application of machine-learning techniques.
