A representation theory perspective on simultaneous alignment and classification

Roy R. Lederman, Amit Singer

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Single particle cryo-electron microscopy (EM) is a method for determining the 3-D structure of macromolecules from many noisy 2-D projection images of individual macromolecules whose orientations and positions are random and unknown. The problem of orientation assignment for the images motivated work on multireference alignment. The recent non-unique games framework provides a representation theoretic approach to alignment over compact groups, and offers a convex relaxation with certificates of global optimality in some cases. One of the great opportunities in cryo-EM is studying heterogeneous samples, containing two or more distinct conformations of molecules. Taking advantage of this opportunity presents an algorithmic challenge: determining both the class and orientation of each particle. We generalize multireference alignment to a problem of alignment and classification, and propose to extend non-unique games to the problem of simultaneous alignment and classification with the goal of simultaneously classifying cryo-EM images and aligning them within their classes.

Original languageEnglish (US)
Pages (from-to)1001-1024
Number of pages24
JournalApplied and Computational Harmonic Analysis
Issue number3
StatePublished - Nov 2020

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


  • Alignment
  • Classification
  • Cryo-em
  • Graph-cut
  • Heterogeneity
  • Heterogeneous multireference alignment
  • Rotation group
  • SDP
  • Synchronization

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