一种改进的局部线性嵌入算法

局部线性嵌入算法(Local Linear Embedding,简称LLE)是一种非线性流形学习算法,能有效地学习出高维采样数据的低维嵌入坐标,但也存在一些不足,如不能处理稀疏的样本数据.针对这些缺点,提出了一种基于局部映射的线性嵌入算法(Local Project Linear Embedding,简称LPLE).通过假定目标空间的整体嵌入函数,重新构造样本点的局部邻域特征向量,最后将问题归结为损失矩阵的特征向量问题从而构造出目标空间的全局坐标.LPLE算法解决了传统LLE算法在源数据稀疏情况下的不能有效进行降维的问题,这也是其他传统的流形学习算法没有解决的.通过实验说明了LPLE算法研究的有效性和意义.

A Better Scaled Local Line Embedding Algorithm

The local linear embedding algorithm is a nonlinear manifold learning algorithm.It is efficient for many nonlinear dimension reduction problems but unfit for sparse data.In this paper,an improved algorithm called local project linear embedding(LPLE) is presented,which is based on local smooth theory and LLE.In the algorithm,assumes a global embedding function in low dimentional space,then reconstructs sample data's local neighbor eigenvector.At last,the global low-dimensional embedded manifold is obtained by eigenvector of the cost matrix.LPLE is better than LLE in that it gives the global coordinates of the sparse data and this isn't be resolved by the other conventional algorithm.The results of experiment show the usefulness and the meaning of the research.