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The proliferation of optical, electron, and scanning probe microscopies givesrise to large volumes of imaging data of objects as diversified as cells,bacteria, pollen, to nanoparticles and atoms and molecules. In most cases, theexperimental data streams contain images having arbitrary rotations andtranslations within the image. At the same time, for many cases, small amountsof labeled data are available in the form of prior published results, imagecollections, and catalogs, or even theoretical models. Here we develop anapproach that allows generalizing from a small subset of labeled data with aweak orientational disorder to a large unlabeled dataset with a much strongerorientational (and positional) disorder, i.e., it performs a classification ofimage data given a small number of examples even in the presence of adistribution shift between the labeled and unlabeled parts. This approach isbased on the semi-supervised rotationally invariant variational autoencoder(ss-rVAE) model consisting of the encoder-decoder "block" that learns arotationally (and translationally) invariant continuous latent representationof data and a classifier that encodes data into a finite number of discreteclasses. The classifier part of the trained ss-rVAE inherits the rotational(and translational) invariances and can be deployed independently of the otherparts of the model. The performance of the ss-rVAE is illustrated using thesynthetic data sets with known factors of variation. We further demonstrate itsapplication for experimental data sets of nanoparticles, creating nanoparticlelibraries and disentangling the representations defining the physical factorsof variation in the data. The code reproducing the results is available athttps://github.com/ziatdinovmax/Semi-Supervised-VAE-nanoparticles.

Semi-supervised learning of images with strong rotational disorder: assembling nanoparticle libraries