  Recently, several data analytic techniques based on connection graph
laplacian (CGL) ideas have appeared in the literature. At this point, the
properties of these methods are starting to be understood in the setting where
the data is observed without noise. We study the impact of additive noise on
these methods, and show that they are remarkably robust. As a by-product of our
analysis, we propose modifications of the standard algorithms that increase
their robustness to noise. We illustrate our results in numerical simulations.
