Dimensionality Reduction Algorithm Based on Manifold Learning

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.