Fig 1. Strategy for unsupervised single-particle clustering via statistical manifold learning.

(A) The fundamental principle of GTM is to establish a numerical relationship between variables in the latent space and a non-Euclidean manifold composed of the Fourier transformed image data in the data space. The manifold embedding can be determined by a set of nonlinear basis functions and a weighted parametric matrix. The likelihood function for the nonlinear mapping is solved by the expectation-maximization algorithm. (B) The workflow of implementing the unsupervised clustering strategies in ROME is as follows: (I) All images are aligned using MAP2D in a reference-free manner, and are subsequently classified into many groups by unsupervised GTM. (II) The unsupervised classes obtained in step (I) are further classified into many sub-classes by unsupervised GTM in a hierarchical fashion.