基于几何距离摄动的局部线性嵌入算法

摘要

The traditional Local Linear Embedding(LLE) algorithm is sensitive for the number of nearest neighbors, and fails on sparse source data. In order to solve this problem, a local linear embedding algorithm based on the geometric distance perturbation is proposed. The local linear property of the manifold data is described by geometric distance perturbation. The original dataset is set into some maximal linear block according to the perturbation. The LLE is applied to this maximal linear patch to complete the embedding dimensional-reduction. Experimental results demonstrate this method can raise the average accurate rate.%传统局部线性嵌入(LLE)算法对近邻个数依赖性较强,不适用于处理稀疏数据源.针对该问题,提出一种基于几何距离摄动的LLE算法.通过线性块内的最大欧氏距离与测地距离之差构造几何摄动,描述流形数据的局部线性特性,对原始流形数据进行最大线性分块操作,保证局部模块的线性特性,并在每一个局部线性模块上应用LLE算法实现嵌入降维.实验结果表明,该算法能有效提高分类的平均准确率.