Open Access
February 2016 Graph connection Laplacian methods can be made robust to noise
Noureddine El Karoui, Hau-Tieng Wu
Ann. Statist. 44(1): 346-372 (February 2016). DOI: 10.1214/14-AOS1275


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.


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Noureddine El Karoui. Hau-Tieng Wu. "Graph connection Laplacian methods can be made robust to noise." Ann. Statist. 44 (1) 346 - 372, February 2016.


Received: 1 May 2014; Revised: 1 September 2014; Published: February 2016
First available in Project Euclid: 5 January 2016

zbMATH: 1350.60036
MathSciNet: MR3449771
Digital Object Identifier: 10.1214/14-AOS1275

Primary: 60F99
Secondary: 53A99

Keywords: concentration of measure , graph connection Laplacian , kernel methods , random matrices , spectral geometry , vector diffusion maps

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 1 • February 2016
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