:流形学习是一种新的非监督学习方法,近年来引起越来越多机器学习和认知科学工作者的重视. 为了加深

对流形学习的认识和理解,该文由流形学习的拓扑学概念入手,追溯它的发展过程. 在明确流形学习的不同表示方

法后,针对几种主要的流形算法,分析它们各自的优势和不足,然后分别引用Isomap 和LL E 的应用示例. 结果表明,

流形学习较之于传统的线性降维方法,能够有效地发现非线性高维数据的本质维数,利于进行维数约简和数据分

析. 最后对流形学习未来的研究方向做出展望,以期进一步拓展流形学习的应用领域.-As a new unsupervised learning met hod , manifold learning is capt uring increasing interest s of re2

searchers in the field of machine learning and cognitive sciences. To under stand manifold learning bet ter ,

t he topology concept of manifold learning was presented firstly , and t hen it s development history was

t raced. Based on different representations of manifold , several major algorit hms were int roduced , whose

advantages and defect s were pointed out respectively. Af ter that , two kinds of typical applications of Iso2

map and LL E were indicated. The result s show that compared wit h t raditional linear method , manifold

learning can discover t he int rinsic dimensions of nonlinear high2dimensional data effectively , helping re2

searchers to reduce dimensionality and analyze data bet ter . Finally t he prospect of manifold learning was

discussed , so as to extend t he application area of manifold learning.