OPTIMAL PROPERTIES OF CENTROID-BASED CLASSIFIERS FOR VERY HIGH-DIMENSIONAL DATA

• 成果类型: Article
• 署名作者: Hall, Peter; Pham, Tung
• 署名单位: University of Melbourne
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS736
• 发表日期: 2010
• 页码: 1071-1093
• 关键词: range correlations; CLASSIFICATION

摘要

We show that scale-adjusted versions of the centroid-based classifier enjoys optimal properties when used to discriminate between two very high-dimensional populations where the principal differences are in location. The scale adjustment removes the tendency of scale differences to confound differences in means. Certain other distance-based methods, for example, those founded on nearest-neighbor distance, do not have optimal performance in the sense that we propose. Our results permit varying degrees of sparsity and signal strength to be treated, and require only mild conditions on dependence of vector components. Additionally, we permit the marginal distributions of vector components to vary extensively. In addition to providing theory we explore numerical properties of a centroid-based classifier, and show that these features reflect theoretical accounts of performance.