Connection graph Laplacian methods can be made robust to noise

TL;DR

This paper investigates the robustness of connection graph Laplacian methods to additive noise, demonstrating their resilience and proposing modifications to enhance noise robustness, supported by numerical simulations.

Contribution

The paper analyzes the impact of noise on CGL methods and introduces algorithmic modifications to improve their robustness against noise.

Findings

CGL methods are surprisingly robust to additive noise

Proposed modifications enhance noise robustness of CGL algorithms

Numerical simulations confirm improved performance under noisy conditions

Abstract

Recently, several data analytic techniques based on connection graph laplacian (CGL) 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.