Wasserstein K-Means for Clustering Tomographic Projections

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.