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

Yulong Zhuang, Salah Awel, Anton Barty, Richard Bean, Johan Bielecki, Martin Bergemann, Benedikt J. Daurer, Tomas Ekeberg, Armando D. Estillore, Hans Fangohr, Klaus Giewekemeyer, Mark S. Hunter, Mikhail Karnevskiy, Richard A. Kirian, Henry Kirkwood, Yoonhee Kim, Jayanath Koliyadu, Holger Lange, Romain Letrun, Jannik LübkeAbhishek Mall, Thomas Michelat, Andrew J. Morgan, Nils Roth, Amit K. Samanta, Tokushi Sato, Zhou Shen, Marcin Sikorski, Florian Schulz, John C.H. Spence, Patrik Vagovic, Tamme Wollweber, Lena Worbs, P. Lourdu Xavier, Oleksandr Yefanov, Filipe R.N.C. Maia, Daniel A. Horke, Jochen Küpper, N. Duane Loh, Adrian P. Mancuso, Henry N. Chapmanc, Kartik Ayyera

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 the fact that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. Proposed here are 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. Both these methods are implemented in combination with the noise-tolerant expand-maximize-compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern. Both discrete structural classes and continuous deformations are recovered. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility of moving beyond the study of homogeneous sample sets to addressing open questions on topics such as nanocrystal growth and dynamics, as well as phase transitions which have not been externally triggered.

Original languageEnglish (US)
Pages (from-to)204-214
Number of pages11
StatePublished - Mar 1 2022


  • XFELs.
  • coherent X-ray diffractive imaging (CXDI)
  • single particles

ASJC Scopus subject areas

  • General Chemistry
  • Biochemistry
  • General Materials Science
  • Condensed Matter Physics


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