Spectral Connectivity Analysis

• 成果类型: Article
• 署名作者: Lee, Ann B.; Wasserman, Larry
• 署名单位: Carnegie Mellon University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2010.tm09754
• 发表日期: 2010
• 页码: 1241-1255
• 关键词: dimensionality reduction; CONVERGENCE; graph; set

摘要

Spectral kernel methods are techniques or mapping data into a coordinate system that efficiently reveals the geometric structure-in particular, the connectivity-of the data. These methods depend on tuning parameters. We analyze the dependence of the method on these tuning parameters. We focus on one particular technique-diffusion maps-but our analysis can be used for other spectral methods as well. We identify the key population quantities, we define an appropriate risk function for analyzing the estimators, and we explain how these methods relate to classical kernel smoothing. We also show that, in some cases, fast rates of convergence are possible even in high dimensions. The Appendix of the article is available online as supplementary materials.