Extremal, properties of principal curves in the plane
成果类型：
Article
署名作者：
Duchamp, T; Stuetzle, W
署名单位：
University of Washington; University of Washington Seattle
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
1996
页码：
1511-1520
关键词：
摘要：
Principal curves were introduced to formalize the notion of ''a curve passing through the middle of a dataset.'' Vaguely speaking, a curve is said to pass through the middle of a dataset if every point on the curve is the average of the observations projecting onto it. This idea can be made precise by defining principal curves for probability densities. In this paper we study principal curves in the plane. Like linear principal components, principal curves are critical points of the expected squared distance from the data. However, the largest and smallest principal components are extrema of the distance, whereas all principal curves are saddle points. This explains why cross-validation does not appear to be a viable method for choosing the complexity of principal curve estimates.