%0 Journal Article
%T Mathematics Properties of HS Principal Curves<br>HS主曲线的数学特性
%A WANG Zhen
%A MIAO Duo-Qian
%A ZHANG Hong-Yun
%A <br>王真
%A 苗夺谦
%A 张红云
%J 计算机科学
%D 2005
%I 
%X Principal Curves have been defined as'self-consistent' smooth curves passing through the middle of a mul- tidimensional data set. They are nonlinear generalizations of the first principal component, which are optimal linear 1- d generalizations of the data. HS principal curves emphasize on the nonparameteried model, in this paper we discuss and prove the nonparametric property. Besides this, the goal of this paper is to further contribute to the theoretical understanding of principal curves,we analysize the transveriality of the principal curves in the 3-d Eulid space.
%K Principal curves
%K Self-consistency
%K Nonparameteric property
%K Transveriality<br>HS主曲线
%K 数学特性
%K 参数无关性
%K 自相合
%K 横截性
%K 横截性质
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=64A12D73428C8B8DBFB978D04DFEB3C1&aid=DADA76A90C140FBE&yid=2DD7160C83D0ACED&vid=9971A5E270697F23&iid=CA4FD0336C81A37A&sid=D46BA3D3D4B3C585&eid=50BBDFAC8381694B&journal_id=1002-137X&journal_name=计算机科学&referenced_num=2&reference_num=11