Graph connection Laplacian methods can be made robust to noise

Noureddine El Karoui; Hau Tieng Wu

doi:10.1214/14-AOS1275

Graph connection Laplacian methods can be made robust to noise

Noureddine El Karoui, Hau Tieng Wu

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	346-372
Number of pages	27
Journal	Annals of Statistics
Volume	44
Issue number	1
DOIs	https://doi.org/10.1214/14-AOS1275
State	Published - Feb 1 2016

Keywords

Concentration of measure
Graph connection Laplacian
Kernel methods
Random matrices
Spectral geometry
Vector diffusion maps

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/14-AOS1275

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N2 - 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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KW - Random matrices

KW - Spectral geometry

KW - Vector diffusion maps

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Graph connection Laplacian methods can be made robust to noise

Abstract

Keywords

ASJC Scopus subject areas

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