Wasserstein K-Means for Clustering Tomographic Projections

Abstract

Motivated by the 2D class averaging problem in single-particle cryo-electron microscopy (cryo-EM), we present a k-means algorithm based on a rotationally-invariant Wasserstein metric for images. Unlike existing methods that are based on Euclidean ($L_2$) distances, we prove that the Wasserstein metric better accommodates for the out-of-plane angular differences between different particle views. We demonstrate on a synthetic dataset that our method gives superior results compared to an $L_2$ baseline. Furthermore, there is little computational overhead, thanks to the use of a fast linear-time approximation to the Wasserstein-1 metric, also known as the Earthmover's distance.

arXiv comment11 pages, 5 figures, 1 table

References in corpus (5)

• Fast Computation of Wasserstein Barycenters
• Hyper-Molecules: on the Representation and Recovery of Dynamical Structures, with Application to Flexible Macro-Molecular Structures in Cryo-EM
• Common lines modeling for reference free ab-initio reconstruction in cryo-EM
• Reconstructing continuous distributions of 3D protein structure from cryo-EM images
• Earthmover-based manifold learning for analyzing molecular conformation spaces

Cited by in corpus (1)

• Manifold learning with arbitrary norms