【摘要】 主曲线是穿过数据云“中间”的满足自相合性质的光滑曲线,它是线性主成分的非线性推广。在本文中,基于主曲线的自相合条件,构造一个微分方程,通过求解这个微分方程,我们得到了环形均匀分布的主曲线;通过对实验结果的分析与研究,我们得出了一些有趣的结论。更多还原

【Abstract】 A principal curve which satisfies the self-consistency property is a smooth curve passing through the "mid- dle" of a dataset, which can be regard as a noulinear generalization of linear principal components. In this paper, we construct a differential equation on the basis of the self-consistency condition of principal curves, and by solving this differential equation, we obtain principal curves for uniform densities on annuli; through analyses and studies of the experimentation’s findings, we have drawn some interesting conclusions.更多还原