Probabilistic PolarGMM: Unsupervised Cluster Learning of Very Noisy Projection Images of Unknown Pose

A crucial step in single particle analysis (SPA) of cryogenic electron microscopy (Cryo-EM), 2D classification and alignment takes a collection of noisy particle images to infer orientations and group similar images together. Averaging these aligned and clustered noisy images produces a set of clean images, ready for further analysis such as 3D reconstruction. Fourier-Bessel steerable principal component analysis (FBsPCA) enables an efficient, adaptable, low-rank rotation operator. We extend the FBsPCA to additionally handle translations. In this extended FBsPCA representation, we use a probabilistic polar-coordinate Gaussian mixture model to learn soft clusters in an unsupervised fashion using an expectation maximization (EM) algorithm. The obtained rotational clusters are thus additionally robust to the presence of pairwise alignment imperfections. Multiple benchmarks from simulated Cryo-EM datasets show probabilistic PolarGMM's improved performance in comparisons with standard single-particle Cryo-EM tools, EMAN2 and RELION, in terms of various clustering metrics and alignment errors.