Another look at principal curves and surfaces
Another look at principal curves and surfaces
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DOI：
10.1006/jmva.2000.1917
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发表时间：
2001-04-01
影响因子：
1.6
通讯作者：
Delicado, P
中科院分区：
文献类型：
--
作者：
Delicado, P
主曲线被定义为通过多维数据集“中间”的平滑曲线。它们是第一主成分的非线性推广。其特征是主曲线定义的基础。我们建立了第一主成分的新特征，并在此基础上给出了主曲线的新定义。引入了主定向点的概念，并证明了经过这些点的主曲线的存在性。我们将主曲线的定义推广到多元数据集，并提出了一种求主曲线的算法。这些新概念使我们对总方差的定义进行了推广。连续的主曲线是由这种推广递归地定义的。在模拟数据集和实际数据集上对新方法进行了说明。(C) 2001学术出版社。
Principal curves have been defined as smooth curves passing through the "middle" of a multidimensional data set. They are nonlinear generalizations of the first principal component. a characterization of which is the basis of the definition of principal curves. We establish a new characterization of the first principal component and base our new definition of a principal curve on this property. We introduce the notion of principal oriented points and we prove the existence of principal curves passing through these points. We extend the definition of principal curves to multivariate data sets and propose an algorithm to find them. The new notions lead us to generalize the definition of total variance. Successive principal curves are recursively defined from this generalization. The new methods are illustrated on simulated and real data sets. (C) 2001 Academic Press.