Properties Analysis and Research of Principal Curves Based on Self-Consistency
基于自相合性的主曲线的特性分析与研究

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.