一种基于线性插值的流形学习算法

A manifold learning algorithm based on linear interpolation technique

作为一种有效的非线性降维方法,流形学习在众多领域引起了广泛关注并取得了长足发展。但当样本点较为稀疏时,样本点的局部邻域很难满足流形学习局部同胚的前提条件,此时流形学习算法往往效果变差甚至失效。一种有效的解决方法是增加一些新的插值点。为此,提出了一种基于三角形重心线性插值技术的流形学习算法。实验结果表明,插值算法能改善样本点的局部结构。将插值算法应用到经典的流形学习算法如LTSA后,实验结果证实了算法的有效性和稳定性。

As an effective non-linear dimension reduction method,manifold learning has attracted widespread attention and experienced a rapid development.But when sample points are not dense this algorithm often becomes worse or even fails just because the points in some neighborhoods do not meet the requirement of local home-omorphism.An effective solution to this problem is to increase some new interpolation method which makes use of the gravity center of triangle in the neighborhood.Experimental results demonstrate the improvement of the neighborhood structure.The effectiveness and stability of our algorithm are further confirmed by the application of it to such classical manifold learning algorithms as LTSA.