Bootstrapping for Significance of Compact Clusters in Multidimensional Datasets

• 成果类型: Article
• 署名作者: Maitra, Ranjan; Melnykov, Volodymyr; Lahiri, Soumendra N.
• 署名单位: Iowa State University; Iowa State University; North Dakota State University Fargo; Texas A&M University System; Texas A&M University College Station
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2011.646935
• 发表日期: 2012
• 页码: 378-392
• 关键词: dimension

摘要

This article proposes a bootstrap approach for assessing significance in the clustering of multidimensional datasets. The procedure compares two models and declares the more complicated model a better candidate if there is significant evidence in its favor. The performance of the procedure is illustrated on two well-known classification datasets and comprehensively evaluated in terms of its ability to estimate the number of components via extensive simulation studies, with excellent results. The methodology is also applied to the problem of k-means color quantization of several standard images in the literature and is demonstrated to be a viable approach for determining the minimal and optimal numbers of colors needed to display an image without significant loss in resolution. Additional illustrations and performance evaluations are provided in the online supplementary material.