LLE算法及其应用

Arithmetic of Locally Linear Embedding and Its Application

LLE算法针对非线性降维问题,利用线性重构的局部对称性找出高维数据空间中的非线性结构。并在保持各数据点临近位置关系情况下,把高维空间数据点映射为低维空间对应的数据点。其计算步骤包括:计算、寻找数据点或邻居数据点、构造数据点及计算权值矩阵,并通过权值矩阵计算低维向量。

Aiming at the problem of nonlinear dimensionality reduction, local linear embedding (LLE) algorithm was presented. The nonlinear structure in high dimensional data space was exploited with the local symmetries of linear reconstructions. The data points in high dimensional space were mapped into corresponding data points in lower dimensional space under preserving distance between data points. The process of LLE algorithm includes calculating, searching data points or border upon data points, creating data points and calculating right value matrix, and the lower dimensional vectors computed through right value matrix.