  We use a recently developed interpretable and unsupervised machine-learning
method, the tensorial kernel support vector machine (TK-SVM), to investigate
the low-temperature classical phase diagram of a generalized
Heisenberg-Kitaev-$\Gamma$ ($J$-$K$-$\Gamma$) model on a honeycomb lattice.
Aside from reproducing phases reported by previous quantum and classical
studies, our machine finds a hitherto missed nested zigzag-stripy order and
establishes the robustness of a recently identified modulated $S_3 \times Z_3$
phase, which emerges through the competition between the Kitaev and $\Gamma$
spin liquids, against Heisenberg interactions. The results imply that, in the
restricted parameter space spanned by the three primary exchange interactions
-- $J$, $K$, and $\Gamma$, the representative Kitaev material $\alpha$-${\rm
RuCl}_3$ lies close to the interface of several phases, including a simple
ferromagnet, and the unconventional $S_3 \times Z_3$ and nested zigzag-stripy
magnets. A zigzag order is stabilized by a finite $\Gamma^{\prime}$ and/or
$J_3$ term, whereas the four magnetic orders may compete in particular if
$\Gamma^{\prime}$ is anti-ferromagnetic.
