  Classification of topological phononics is challenging due to the lack of
universal topological invariants and the randomness of structure patterns.
Here, we show the unsupervised manifold learning for clustering topological
phononics without any priori knowledge, neither topological invariants nor
supervised trainings, even when systems are imperfect or disordered. This is
achieved by exploiting the real-space projection operator about finite phononic
lattices to describe the correlation between oscillators. We exemplify the
efficient unsupervised manifold clustering in typical phononic systems,
including one-dimensional Su-Schrieffer-Heeger-type phononic chain with random
couplings, amorphous phononic topological insulators, higher-order phononic
topological states and non-Hermitian phononic chain with random dissipations.
The results would inspire more efforts on applications of unsupervised machine
learning for topological phononic devices and beyond.
