  The deep connection among braids, knots and topological physics has provided
valuable insights into studying topological states in various physical systems.
However, identifying distinct braid groups and knot topology embedded in
non-Hermitian systems is challenging and requires significant efforts. Here, we
demonstrate that an unsupervised learning with the representation basis of
$su(n)$ Lie algebra on $n$-fold extended non-Hermitian bands can fully classify
braid group and knot topology therein, without requiring any prior mathematical
knowledge or any pre-defined topological invariants. We demonstrate that the
approach successfully identifies different topological elements, such as
unlink, unknot, Hopf link, Solomon ring, trefoil, and so on, by employing
generalized Gell-Mann matrices in non-Hermitian models with $n$=2 and $n$=3
energy bands. Moreover, since eigenstate information of non-Hermitian bands is
incorporated in addition to eigenvalues, the approach distinguishes the
different parity-time symmetry and breaking phases, recognizes the opposite
chirality of braids and knots, and identifies out distinct topological phases
that were overlooked before. Our study shows significant potential of machine
learning in classification of knots, braid groups, and non-Hermitian
topological phases.
