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A shift-invariant variational autoencoder (shift-VAE) is developed as anunsupervised method for the analysis of spectral data in the presence of shiftsalong the parameter axis, disentangling the physically-relevant shifts fromother latent variables. Using synthetic data sets, we show that the shift-VAElatent variables closely match the ground truth parameters. The shift VAE isextended towards the analysis of band-excitation piezoresponse force microscopy(BE-PFM) data, disentangling the resonance frequency shifts from the peak shapeparameters in a model-free unsupervised manner. The extensions of this approachtowards denoising of data and model-free dimensionality reduction in imagingand spectroscopic data are further demonstrated. This approach is universal andcan also be extended to analysis of X-ray diffraction, photoluminescence, Ramanspectra, and other data sets.

Decoding the shift-invariant data: applications for band-excitation scanning probe microscopy