Mathematics Properties of HS Principal Curves
HS主曲线的数学特性

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.