基于流形学习的非线性维数约简方法  

Nonlinear Dimensionality Reduction Method Based on Manifold Learning

作　　者：段志臣[1] 芮小平[2] 张立媛[3] 

机构地区：[1]中国矿业大学(北京)理学院,北京100083 [2]中国科学院研究生院资源与环境学院,北京100049 [3]国立华侨大学工商管理学院,福建泉州362000

出　　处：《数学的实践与认识》2012年第8期230-241,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(40901191)

摘　　要：流形学习是一种新的非线性维数约简方法,近年来正引起可视化等领域研究者的高度重视.为加深对流形学习的理解,介绍了流形学习的基本原理,总结了其研究进展和分类方法,最后阐述了几种常用的流形学习方法的基本思想、算法步骤和各自的优缺点.通过在人工数据集Swiss-Roll上进行实验,将各类方法在近邻值选取和噪声影响等方面进行了对比分析,结果表明:与传统的线性维数约简方法相比,流形学习方法能够有效地发现观测样本的低维结构.最后对流形学习未来的研究方向作出展望,以期在这一领域取得更大进展.As a new kind of nonlinear dimensionality reduction method,manifold learning is capturing increasing interests of researchers.To understand manifold learning better,the principle is firstly introduced,and then its development history and different representations are summarized,finally several major method are introduced,whose basic thoughts,steps and advantages are pointed out respectively.By the experiments on Swiss-Roll,the selection of neighbors and noise effect are analyzed,the results shows：compared with traditional linear method,manifold learning can discover the intrinsic structure of the samples better.Finally the prospect of manifold learning was discussed for more developments.

关 键 词：维数约简 流形学习 谱图理论 等距映射 局部线性嵌入 

分 类 号：O189[理学—数学]