Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality.
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.
Mathematically, if the parameter space of each continuous independent motion is a manifold, then their combination is known as a product manifold.
Single-particle cryo-Electron Microscopy (EM) has become a popular technique for determining the structure of challenging biomolecules that are inaccessible to other technologies.
In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction.
An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform.
The resulting classifier is linear in the log-transformed univariate and bivariate densities that correspond to the tree edges.