Distance shrinkage and Euclidean embedding via regularized kernel estimation

• 成果类型: Article
• 署名作者: Zhang, Luwan; Wahba, Grace; Yuan, Ming
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12138
• 发表日期: 2016
• 页码: 849-867
• 关键词: nonlinear dimension reduction; semidefinite; algorithm; matrices

摘要

Although recovering a Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based on the so-called regularized kernel estimate. We show that such an estimate can be characterized as simply applying a constant amount of shrinkage to all observed pairwise distances. This fact allows us to establish risk bounds for the estimate, implying that the true distances can be estimated consistently in an average sense as the number of objects increases. In addition, such a characterization suggests an efficient algorithm to compute the distance matrix estimator, as an alternative to the usual second-order cone programming which is known not to scale well for large problems. Numerical experiments and an application in visualizing the diversity of Vpu protein sequences from a recent study of human immunodeficiency virus type 1 further demonstrate the practical merits of the method proposed.