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第 1 卷第 1 期智能系统学报 Vol. 1 №. 1
2006 年 3 月 CAA I Transactions on Intelligent Systems Mar. 2006
流形学****概述
徐蓉,姜峰,姚鸿勋
(哈尔滨工业大学计算机科学与技术学院,黑龙江哈尔滨 150001)
摘要:流形学****是一种新的非监督学****方法,近年来引起越来越多机器学****和认知科学工作者的重视. 为了加深
对流形学****的认识和理解,该文由流形学****的拓扑学概念入手,追溯它的发展过程. 在明确流形学****的不同表示方
法后,针对2 几2 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****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****未来的研究方向做出展望,以期进一步拓展流形学****的应用领域.
关键词:维数约简;流形学****等距离映射算法;局部线性嵌入算法;交叉流形
中图分类号: TP181 文献标识码:A 文章编号:1673 4785 (2006) 01 0044 08
Overview of manifold learning
XU Rong ,J IAN G Feng , YAO Hong xun
(School puter Science and Technology , Harbin Institute of Technology , Harbin 150001 ,China)
Abstract :As a new unsupervised learning met hod , manifold learning is capt uring increasing interest s of re
searchers in the field of machine learning and cognitive sciences. To understand manifold learning better ,
t he topology concept of manifold learning was presented firstly , and t hen it s develop ment history was
traced. Based on different representations of manifold , several major algorit hms were introduced , whose
advantages and defect s were pointed out respectively. After that , two kinds of typical applications of Iso
map and LL E were indicated. The result s show pared wit h traditional linear method , manifold
learning can discover t he intrinsic dimensions of
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第 1 卷第 1 期智能系统学报 Vol. 1 №. 1
2006 年 3 月 CAA I Transactions on Intelligent Systems Mar. 2006
流形学****概述
徐蓉,姜峰,姚鸿勋
(哈尔滨工业大学计算机科学与技术学院,黑龙江哈尔滨 150001)
摘要:流形学****是一种新的非监督学****方法,近年来引起越来越多机器学****和认知科学工作者的重视. 为了加深
对流形学****的认识和理解,该文由流形学****的拓扑学概念入手,追溯它的发展过程. 在明确流形学****的不同表示方
法后,针对2 几2 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****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****未来的研究方向做出展望,以期进一步拓展流形学****的应用领域.
关键词:维数约简;流形学****等距离映射算法;局部线性嵌入算法;交叉流形
中图分类号: TP181 文献标识码:A 文章编号:1673 4785 (2006) 01 0044 08
Overview of manifold learning
XU Rong ,J IAN G Feng , YAO Hong xun
(School puter Science and Technology , Harbin Institute of Technology , Harbin 150001 ,China)
Abstract :As a new unsupervised learning met hod , manifold learning is capt uring increasing interest s of re
searchers in the field of machine learning and cognitive sciences. To understand manifold learning better ,
t he topology concept of manifold learning was presented firstly , and t hen it s develop ment history was
traced. Based on different representations of manifold , several major algorit hms were introduced , whose
advantages and defect s were pointed out respectively. After that , two kinds of typical applications of Iso
map and LL E were indicated. The result s show pared wit h traditional linear method , manifold
learning can discover t he intrinsic dimensions of
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