GRAPH CONNECTION LAPLACIAN METHODS CAN BE MADE ROBUST TO NOISE

• 成果类型: Article
• 署名作者: El Karoui, Noureddine; Wu, Hau-Tieng
• 署名单位: University of California System; University of California Berkeley; University of Toronto
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1275
• 发表日期: 2016
• 页码: 346-372
• 关键词: eigenvector synchronization; diffusion maps; REPRESENTATION

摘要

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.