中山大学学报（自然科学版）Issue(5)：82-90,96,10.
一种基于Biharmonic样条插值的流形学习算法*
A Manifold Learning Algorithm Based on Biharmonic Spline Interpolation Technique
摘要
Abstract
As an effective non-linear dimension reduction method,manifold learning has attracted wide-spread attention and made great progress.But when sample points are not dense,these algorithms often become worse or even failed just because the points in some neighborhoods do not meet the requirement of local homeomorphism.An effective solution to this question is to increase some new interpolation points. Unfortunately,the points selected by existing interpolation methods nowadays are all linear with the origi-nal sample points.From the theory of linear algebra,the subspace spanned by the interpolation points and the original neighbors is the same as the subspace spanned by the original ones;therefore,the inter-polation points will not improve the linear approximation error either.Moreover,the interpolation points have no consideration to the native structure and characteristics of the manifold,which deviates from the purpose of data dimensionality reduction.To this end,a new manifold learning algorithm based on a non-linear interpolation method called Biharmonic is proposed.Experimental results demonstrate the improve-ment of the neighborhood structure.The effectiveness and stability of this algorithm are further confirmed by applying it to the classical manifold learning algorithms.关键词
流形学习/数据降维/曲面拟合/插值Key words
manifold learning/dimensionality reduction/surface fitting/interpolation分类
信息技术与安全科学引用本文复制引用
顾艳春,马争鸣,梁宇滔..一种基于Biharmonic样条插值的流形学习算法*[J].中山大学学报（自然科学版）,2013,(5):82-90,96,10.基金项目
广东省自然科学基金资助项目（8452800001001086）；佛山科学技术学院资助项目 （）
