具有局部结构保留性质的PCA改进算法

保局投影(LPP)是一种局部结构保留算法，它使得每个数据点和它的近邻点在投影空间中尽可能地保持相近.结合LPP的几何思想，本文提出一种具有局部结构保留特性的PCA改进算法——保局PCA(LP-PCA).该算法通过构造数据集的邻接图及其补图，对近邻点和非近邻点采取不同的处理方式.在获得数据集全局结构的同时，可有效保留数据集的局部结构.在模拟数据集和现实数据集上进行实验，实验结果验证该算法的有效性.

An Improved PCA Algorithm with Local Structure Preserving

Locality preserving projection (LPP) is a local structure preserving method and the distances of neighboring points are minimized in the subspace of LPP. Combined with the geometric idea of LPP, an improved PCA with local structure preserving is proposed called locality preserving PCA (LP-PCA). By constructing the neighborhood graph and its complement, LP-PCA deals with the neighboring points and the far points distinguishingly. LP-PCA minimizes the distances between the neighboring points and simultaneously maximizes the distances between the far points. The improved algorithm can find the global structure of the high dimensional dataset with preserving its local structure. Some examples of the improved algorithm are given on toy datasets as well as on actual datasets. Experimental results show the effectiveness of LP-PCA.