  We illustrate how the tensorial kernel support vector machine (TK-SVM) can
probe the hidden multipolar orders and emergent local constraint in the
classical kagome Heisenberg antiferromagnet. We show that TK-SVM learns the
finite-temperature phase diagram in an unsupervised way. Moreover, in virtue of
its strong interpretability, it identifies the tensorial quadrupolar and
octupolar orders, which define a biaxial $D_{3h}$ spin nematic, and the local
constraint that underlies the selection of coplanar states. We then discuss the
disorder hierarchy of the phases, which can be inferred from both the
analytical order parameters and a SVM bias parameter. For completeness we
mention that the machine also picks up the leading $\sqrt{3} \times \sqrt{3}$
correlations in the dipolar channel at very low temperature, which are however
weak compared to the quadrupolar and octupolar orders. Our work shows how
TK-SVM can facilitate and speed up the analysis of classical frustrated
magnets.
