Graph connection Laplacian methods can be made robust to noise
Noureddine El Karoui, Hau-Tieng Wu
The Annals of Statistics · 2016 · Volume 44 · Issue 1
Abstract
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.
Keywords
53A99, 60F99, concentration of measure, graph connection Laplacian, kernel methods, random matrices, spectral geometry, vector diffusion maps
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