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Graph connection Laplacian methods can be made robust to noise. (English) Zbl 1350.60036

Summary: Recently, several data analytic techniques based on graph connection Laplacian (GCL) 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.

MSC:

60F99 Limit theorems in probability theory
60B20 Random matrices (probabilistic aspects)
65C60 Computational problems in statistics (MSC2010)
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