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