Lederman, Roy R; Singer, Amit A representation theory perspective on simultaneous alignment and classification Journal Article Applied and Computational Harmonic Analysis, 49 (3), pp. 1001–1024, 2020, ISSN: 1063-5203. Abstract | Links | BibTeX | Tags: Algorithms, Alignment, Classification, cryo-EM, Graph-cut, heterogeneity, Heterogeneous multireference alignment, Representation Theory, Rotation group, SDP, Synchronization @article{lederman_representation_2020, title = {A representation theory perspective on simultaneous alignment and classification}, author = {Roy R Lederman and Amit Singer}, url = {http://www.sciencedirect.com/science/article/pii/S1063520319301034}, doi = {10.1016/j.acha.2019.05.005}, issn = {1063-5203}, year = {2020}, date = {2020-01-01}, urldate = {2021-01-22}, journal = {Applied and Computational Harmonic Analysis}, volume = {49}, number = {3}, pages = {1001--1024}, abstract = {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.}, keywords = {Algorithms, Alignment, Classification, cryo-EM, Graph-cut, heterogeneity, Heterogeneous multireference alignment, Representation Theory, Rotation group, SDP, Synchronization}, pubstate = {published}, tppubtype = {article} } 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. |