改进的非线性数据降维方法及其应用

局部线性嵌入算法(Locally Linear Embedding,LLE)是基于流形学习的非线性降维方法之一。LLE利用样本点的近邻点的线性组合对每个样本点进行局部重构,而不同近邻个数的选取会产生不同的重构误差,从而影响整体算法的实施。提出了一种LLE的改进算法,算法有效地降低了近邻点个数对算法的影响,并很好地学习了高维数据的流形结构。所提方法的有效性在人造和真实数据的对比实验中得到了证实。

Improved non-linear data dimensionality reduction method and its application

Locally Linear Embedding（LLE） algorithm is one of the non-linear dimensionality reduction methods which are based on manifold learning.In LLE,each sample point is reconstructed from a linear combination of its nearest neighbors.However,different number of neighbors will produce different reconstruction errors,which will make the result different directly.This paper structures the approximate reconstruction coefficient making use of their category information which is obtained by clustering,and proposes an improved algorithm.The proposed algorithm can reduce the influence of the number of neighbors efficiently and the probability of the database is retained.This is confirmed by experiments on both synthetic and real-world data.