文章基本信息

标题：Selecting the length of a principal curve within a Gaussian model
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作者：Aurélie Fischer
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2013
卷号：7
页码：342-363
DOI：10.1214/13-EJS775
语种：English
出版社：Institute of Mathematical Statistics
摘要：Principal curves are parameterized curves passing “through the middle” of a data cloud. These objects constitute a way of generalization of the notion of first principal component in Principal Component Analysis. Several definitions of principal curve have been proposed, one of which can be expressed as a least-square minimization problem. In the present paper, adopting this definition, we study a Gaussian model selection method for choosing the length of the principal curve, in order to avoid interpolation, and obtain a related oracle-type inequality. The proposed method is practically implemented and illustrated on cartography problems.