| HS主曲线的数学特性 |
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| 引用本文： | 王真,苗夺谦,张红云.HS主曲线的数学特性[J].计算机科学,2005,32(1):185-186. |
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| 作者姓名： | 王真 苗夺谦 张红云 |
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| 作者单位： | 同济大学计算机科学与工程系,上海,200092 |
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| 基金项目： | 国家自然科学基金(No.60175016)，上海市教委“曙光计划”项目 |
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| 摘 要： | 主曲线被定义作穿过多维数据分布“中间”的满足“自相合”的光滑曲线，它是第一主成分的非线性推广，第一主成分是对数据集的一维线性最优描递。HS主曲线强调非参数模型，对其参数无关性本文给出了具体证明。同时为了全面理解主曲线，本文以空间主曲线为例，分析了它的横截性质。
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| 关 键 词： | HS主曲线 数学特性 参数无关性 自相合 横截性 横截性质 |
Mathematics Properties of HS Principal Curves |
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| WANG Zhen,MIAO Duo-Qian,ZHANG Hong-Yun.Mathematics Properties of HS Principal Curves[J].Computer Science,2005,32(1):185-186. |
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| Authors: | WANG Zhen MIAO Duo-Qian ZHANG Hong-Yun |
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| Affiliation: | WANG Zhen,MIAO Duo-Qian,ZHANG Hong-Yun Department of Computer Science and Engineering,Tongji University,Shanghai 200092 |
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| Abstract: | 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. |
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| Keywords: | Principal curves Self-consistency Nonparameteric property Transveriality |
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