Unsupervised learning approaches to characterize heterogeneous samples using X-ray single particle imaging

TL;DR

This paper introduces two unsupervised methods, common-line PCA and VAEs, to classify and generate 3D structures from heterogeneous X-ray SPI data, addressing orientation and noise challenges.

Contribution

It presents novel orientation-aware classification and structure generation techniques for heterogeneous X-ray SPI data, enabling analysis of complex structural landscapes.

Findings

Successfully classified structural heterogeneity in experimental data

Generated 3D structures at various points in the structural landscape

Demonstrated robustness with low photon count datasets

Abstract

One of the outstanding analytical problems in X-ray single particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. We propose two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA) provides a rough classification which is essentially parameter-free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs) can generate 3D structures of the objects at any point in the structural landscape. We implement both these methods in combination with the noise-tolerant expand-maximize-compress (EMC) algorithm and demonstrate its utility by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern and recover both discrete structural classes as well as continuous deformations. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility to move beyond studying homogeneous sample sets and study open questions on topics such as nanocrystal growth and dynamics as well as phase transitions which have not been externally triggered.