Connection graph Laplacian methods can be made robust to noise

In the last few years, several interesting variants of kernel-based spectral methods have arisen in the applied mathematics literature. These ideas appeared in connection with new types of data, where pairs of objects or measurements of interest have a relationship that is "blurred" by the action of a nuisance parameter. More specifically, we can find this type of data in a wide range of problems, for instance in the class averaging algorithm for the cryo-electron microscope (cryo-EM) problem [62, 71], in a modern light source imaging technique known as ptychography [45], in graph realization problems [24, 25], in vectored PageRank [20], in multi-channels image processing [5], etc... Before we give further details about the cryo-EM problem, let us present the main building blocks of the methods we will study. They depend on the following three components: 1. an undirected graph G (V, E) which describes all observations.