摘要：

介绍线性维数约简的主成分分析和多维尺度算法，描述几种经典的能发现嵌入在高维数据空间的低维光滑流形非线性维数约简算法，包括等距映射、局部线性嵌入、拉普拉斯特征映射、局部切空间排列、最大方差展开。与线性维数约简算法相比，非线性维数约简算法通过维数约简能够发现不同类型非线性高维数据的本质特征。

关键词: 流形学, 谱图理论, 局部切空间, 特征映射

Abstract:

This paper reviews Principal Components Analysis(PCA) and Multidimensional Scaling(MDS) methods for linear dimensionality reduction. Several classical nonlinear dimensional reduction methods that can find a smooth low-dimensional manifold embedded in the high-dimensional space are described and a number of improvement of these algorithms are introduced, including Isometric Feature Mapping (ISOMAP), Locally Linear Embedding(LLE), Laplacian Eigenmaps, Local Tangent Space Alignment(LTSA), Maximum Variance Unfolding (MVU). Compared with linear methods, nonlinear dimensionality reduction methods in manifold can extract the intrinsic characteristics of different types of high-dimensional data performing nonlinear dimensionality reduction.

Key words: manifold learning, spectral graph theory, local tangent space, eigenmaps

中图分类号: 

• TP312