That's my thinking too. PCA completely ignores the phase shift symmetry and treats a phase-shifted sine wave as a different thing. One could definitely get som

That's my thinking too. PCA completely ignores the phase shift symmetry and treats a phase-shifted sine wave as a different thing. One could definitely get something better if they took the audio-loops as translation-invariant. I thought about trying to do a symmetry-invariant (or 'group-action-invariant') PCA but I could not find a good way of doing that. More advanced methods, e.g. 1-d convolutional networks, WaveNet etc. do have this translation-invariance built into them. Interestingly, the second eigenvector is not just a phase-shifted version of the first eigenvector but contains slightly higher frequency information as well, but I agree totally with what you said.