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- (--) 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 phase, which emerges through the competition between the Kitaev and spin liquids, against Heisenberg interactions. The results imply that, in the restricted parameter space spanned by the three primary exchange interactions -- , , and , the representative Kitaev material - lies close to the boundaries of several phases, including a simple ferromagnet, the unconventional and nested zigzag-stripy magnets. A zigzag order is stabilized by a finite and/or term, whereas the four magnetic orders may compete in particular if is anti-ferromagnetic.
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