The Annals of Statistics

Graph connection Laplacian methods can be made robust to noise

Noureddine El Karoui and Hau-Tieng Wu

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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.

Article information

Source
Ann. Statist., Volume 44, Number 1 (2016), 346-372.

Dates
Received: May 2014
Revised: September 2014
First available in Project Euclid: 5 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.aos/1452004789

Digital Object Identifier
doi:10.1214/14-AOS1275

Mathematical Reviews number (MathSciNet)
MR3449771

Zentralblatt MATH identifier
1350.60036

Subjects
Primary: 60F99: None of the above, but in this section
Secondary: 53A99: None of the above, but in this section

Keywords
Concentration of measure random matrices graph connection Laplacian vector diffusion maps spectral geometry kernel methods

Citation

El Karoui, Noureddine; Wu, Hau-Tieng. Graph connection Laplacian methods can be made robust to noise. Ann. Statist. 44 (2016), no. 1, 346--372. doi:10.1214/14-AOS1275. https://projecteuclid.org/euclid.aos/1452004789


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