  The study of topological bandstructures is an active area of research in
condensed matter physics and beyond. Here, we combine recent progress in this
field with developments in machine-learning, another rising topic of interest.
Specifically, we introduce an unsupervised machine-learning approach that
searches for and retrieves paths of adiabatic deformations between
Hamiltonians, thereby clustering them according to their topological
properties. The algorithm is general as it does not rely on a specific
parameterization of the Hamiltonian and is readily applicable to any symmetry
class. We demonstrate the approach using several different models in both one
and two spatial dimensions and for different symmetry classes with and without
crystalline symmetries. Accordingly, it is also shown how trivial and
topological phases can be diagnosed upon comparing with a generally designated
set of trivial atomic insulators.
