关键词: 流形学习, 局部几何特性, 线性投影, 内在流形, 谱图

Abstract: Local preserving manifold learning algorithms preserve local geometric properties between observed space and intrinsic embedding space from local to global geometry，and find the intrinsic low-dimensional manifold in the high-dimensional Euclidean space.This paper analyzes the fundamental implementation framework of local preserving manifold learning and compares in detail the properties of several classical manifold learning algorithms based on local preserving.Finally，several helpful research directions are proposed.

Key words: manifold learning, local geometry property, linear projection, intrinsic manifold, spectral graph