摘要：

局部线性嵌入算法通常用于高维流形数据降维，具有结构简单、不易陷入局部极小值、能保持局部几何结构不变的特点，但它对噪声和干扰奇异值点非常敏感。为此，提出基于局部超平面的流形奇异值点去除算法，将样本点的邻域投影到超平面空间，使干扰奇异值点投影远离流形样本点投影，而流形样本点投影则表现为聚集特征，同时找出邻域中所有远离聚集中心的样本点作为干扰奇异值点。仿真实验结果验证了该算法的正确性和有效性。

关键词: 局部超平面, 流形, 局部线性嵌入, 奇异值点

Abstract:

Locally Linear Embedding(LLE) algorithm is typically used to reduce dimensionality of high-dimensional manifold data. Though it has advantage such as a simple structure, being not easy to fall into local minimum value and preserving the same local geometric structure, the algorithm is sensitive to the noise points and singular value points. To solve this problem, this paper presents a locally hyperplane algorithm which can remove the singular value points. The algorithm projects each neighborhood of sample points onto the hyperplane space, so the projections of singular value points will be away from other projections that are aggregate in the neighborhood, and it finds all the points that are away from the gathering center in the neighborhood as singular value points. Simulation results verify the validity and effectiveness of the algorithm.

Key words: locally hyperplane, manifold, Locally Linear Embedding(LLE), singular value point

中图分类号: 

• TP18