[1]徐 蓉,姜 峰,姚鸿勋.流形学习概述[J].智能系统学报,2006,1(01):44-51.
 XU Rong,JIANG Feng,YAO Hong-xun.Overview of manifold learning[J].CAAI Transactions on Intelligent Systems,2006,1(01):44-51.
点击复制

流形学习概述(/HTML)
分享到:

《智能系统学报》[ISSN:1673-4785/CN:23-1538/TP]

卷:
第1卷
期数:
2006年01期
页码:
44-51
栏目:
出版日期:
2006-03-25

文章信息/Info

Title:
Overview of manifold learning
文章编号:
1673-4785(2006)01-0044-08
作者:
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
Author(s):
XU RongJIANG Feng YAO Hong-xun
School of Computer Science and Technology, Harbin Institute of Technology,Ha rbin 150001,China
关键词:
维数约简流形学习等距离映射算法局部线性嵌入算法交叉流形
Keywords:
dimensionality reductionmanifold learningIsomapLLEintersectin g manifold
分类号:
TP181
文献标志码:
A
摘要:
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LLE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.
Abstract:
As a new unsupervised learning method, manifold learning is capturing increasing interests of researchers in the field of machine learning and cogniti ve sciences. To understand manifold learning better, the topology concept of man ifold learning was presented firstly, and then its development history was trace d. Based on different representations of manifold, several major algo rithms were introduced, whose advantages and defects were pointed out resp ectively. After that , two kinds of typical applications of Isomap and LLE were indicated. The res ults show th at compared with traditional linear method, manifold learning can discover the in trinsic dimensions of nonlinear highdimensional data effectively, helping re searchers to reduce dimensionality and analyze data better. Finally the prospect of manifold learning was discussed, so as to extend the application area of man ifold learning.

参考文献/References:

[1] HYVRINEN A. Survey on independent component analysis[J]. Neural Computi ng Surveys , 1999,2(4): 94-128.
[2] TURK M, PENTLAND A. Eigenfaces for recognition[J]. Journal of Cognitive Neuroscience , 1991,3(1):71-86.
[3] GONZALEZ R C, WOODS R E. Digital image processing:2nd ed[M]. Beijing: Publishing House of Electronics Industry, 2003.
[4] SEUNG H S, LEE D D. The manifold ways of perception[J]. Science, 2000,290(5500):2268-2269.
[5] TENENBAUM J, SILVA D D, LANGFORD J. A global geometric framework for nonlinear dimensionality reduction[J]. Science, 2000, 290(5500): 2319-232 3.
[6] ROWEIS S, SAUL L. Nonlinear dimensionality reduction by locally li near embedding[J]. Science, 2000, 290(5500): 2323-2326.
[7] 王守觉. 仿生模式识别(拓扑模式识别)——一种模式识别新模型的理论与应用[J ]. 电子学报, 2002, 30(10):1417-1420.
WANG Shoujue. Bionic(Topological) pattern recognition—a new model of pattern r ecognition theory and its applications[J]. Acta Electronica Sinica, 2002,30(10 ): 1417-1420.
[8] 张军平,曹存根. 神经网络及其应用[M]. 北京: 清华大学出版社, 2 004.
ZHANG Junping, CAO Cungen. Neural network and applications[M]. Beijing: Tsi nghua University Press, 2004.
[9] ZHANG C S, WANG J, ZHAO N Y, ZHANG D. Reconstruction and analysis of multip ose face images based on nonlinear dimensionality reduction[J]. Pattern Recogn ition, 2004,37(1): 325-336.
[10] 詹德川, 周志华. 基于集成的流形学习可视化[J]. 计算机研究与发展, 2005, 4 2 (9): 1533-1537.
ZHAN Dechuan, ZHOU Zhihua. Ensemblebased manifold learning for visuali zatio n[J]. Journal of Computer Research and Development, 2005, 42(9): 1533-1537.
[11] 赵连伟, 罗四维, 赵艳敞,等. 高维数据的低维嵌入及嵌入维数研究[J]. 软件学报, 2005, 16(8): 1423-1430.
 ZHAO Lianwei, LUO Siwei, ZHAO Yanchang, et al. Study on the lowdime nsi onal embedding and the embedding dimensionality of manifold of highdimensional data[J]. Journal of Software, 2005, 16(8): 1423-1430.
[12] 何    力, 张军平, 周志平. 基于放大因子和延伸方向研究流形学习算法[J]. 计算机学报, 2005, 28(12): 2000-2009.
 HE Li, ZHANG Junping, ZHOU Zhiping. Investigating manifold learning algori thms based on magnification factors and principal spread directions[J]. Chinese Jo urnal of Computers, 2005, 28(12): 2000-2009.
[13] BELKIN M, NIYOGI P. Laplacian eigenmaps for dimensionality reducti on and data representation[J]. Neural Computation, 2003, 15(6): 1373-1396.
[14] ZHANG Z Y, ZHA H Y. Principal manifolds and nonlinear dimensionali ty reduc tion via tangent space alignment[J]. SIAM Journal of Scientific Computing, 200 5, 26(1): 313-338.
[15] SIMARD P Y, LECUN Y A, DENKER J S. Efficient pattern recognition using a n ew transformation distance[J]. Advances in Neural Information Processing Syste ms, 1993(5): 50-58.
[16] ZHANG J P, LI S Z, WANG J. Intelligen t Mul timedia Processing with Soft Computing[C]. Heidelberg: Springer-Verlag, 2004. 
[17] HASTIE T, STUETZLE W. Principla Curves[J]. Journal of the Ame rican Statistical Association, 1988, 84(406): 502-516.
[18] K′EGL B, KRZYZAK A, LINDER T, ZEGER K. Learning and design of p rincipal cu rves[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(3): 281-297.
[19] BISHOP C M, SEVENSEN M, WILLIAMS C K I. GTM: The generative top ographic mapping[J]. Neural Computation, 1998,10(1): 215-234.
[20] CHANG K, GHOSH J. A unified model for probabilistic principal s urfaces[ J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(1) : 22-41.
[21] SMOLA A J, MIKA S. Regularized principal manifolds[A]. In Computati onal Learning Theory: 4th European Conference[C]. New York: SpringerVerlag, 1999.
[22] HINTON G, ROWEIS S. Stochastic neighbor embedding[A]. Neur al Informatio n Proceeding Systems: Natural and Synthetic[C]. Vancouver,Canada,2002.
[23] BRAND M, MERL. Charting a manifold[A]. Neural Information Procee ding Systems: Natural and Synthetic[C]. Vancouver,Canada, 2002.
[24] BORG I, GROENEN P. Modern multidimensional scaling: theory and app lication [M]. NewYork: SpringerVerlag, 1997.
[25] MIN W L, LU L, HE X F. Locality pursuit embedding[J]. Pattern Recognit ion, 2004, 37(4): 781-788.
[26] 杨    剑, 李伏欣, 王    珏. 一种改进的局部切空间排列算法[J]. 软件学报, 200 5, 16(9): 1584-1589.
YANG Jian, LI Fuxin, WANG Jue. A better scaled local tangent space align ment algorithm[J]. Journal of Software, 2005,16(9): 1584-1589.
[27] 翁时锋, 张长水, 张学工. 非线性降维在高维医学数据处理中的应用[J]. 清华大学学报(自然科学版), 2004,44(4): 485-488.
WENG Shifeng, ZHANG Changshui, ZHANG Xuegong. Nonlinear dimensionality red uct ion in the analysis of high dimensional medical data[J]. Journal of Tsinghua University(Sci & Tech), 2004, 44(4): 485-488.

相似文献/References:

[1]谢朝霞,穆志纯,谢建军.基于LLE的多姿态人耳识别[J].智能系统学报,2008,3(04):321.
 XIE Zhao-xia,MU Zhi-chun,XIE J ian-jun.Multi-pose ear recogn ition based on locally linear embedding[J].CAAI Transactions on Intelligent Systems,2008,3(01):321.
[2]文贵华,江丽君,文 军.局部测地距离估计的Hessian局部线性嵌入[J].智能系统学报,2008,3(05):429.
 WEN Gui-hua,J IANG L i-jun,WEN Jun.Using locally estimated geodesic distances to improve Hessian local linear embedding[J].CAAI Transactions on Intelligent Systems,2008,3(01):429.
[3]刘 琚,乔建苹.基于学习的超分辨率重建技术[J].智能系统学报,2009,4(03):199.
 LIU Ju,QIAO Jian-ping.Learningbased superresolution reconstruction[J].CAAI Transactions on Intelligent Systems,2009,4(01):199.
[4]谈超,关佶红,周水庚.增量与演化流形学习综述[J].智能系统学报,2012,7(05):377.
 TAN Chao,GUAN Jihong,ZHOU Shuigeng.Incremental and evolutionary manifold learning: a survey[J].CAAI Transactions on Intelligent Systems,2012,7(01):377.
[5]练浩,曾宪华,李淑芳.有监督全局流形排序的图像检索算法[J].智能系统学报,2014,9(01):92.[doi:10.3969/j.issn.1673-4785.201303021]
 LIAN Hao,ZENG Xianhua,LI Shufang.Supervised global manifold ranking based image retrieval algorithm[J].CAAI Transactions on Intelligent Systems,2014,9(01):92.[doi:10.3969/j.issn.1673-4785.201303021]
[6]张钢,谢晓珊,黄英,等.面向大数据流的半监督在线多核学习算法[J].智能系统学报,2014,9(03):355.[doi:10.3969/j.issn.1673-4785.201403067]
 ZHANG Gang,XIE Xiaoshan,HUANG Ying,et al.An online multi-kernel learning algorithm for big data[J].CAAI Transactions on Intelligent Systems,2014,9(01):355.[doi:10.3969/j.issn.1673-4785.201403067]
[7]程旸,王士同.基于局部保留投影的多可选聚类发掘算法[J].智能系统学报,2016,11(5):600.[doi:10.11992/tis.201508022]
 CHENG Yang,WANG Shitong.A multiple alternative clusterings mining algorithm using locality preserving projections[J].CAAI Transactions on Intelligent Systems,2016,11(01):600.[doi:10.11992/tis.201508022]
[8]杨文元.多标记学习自编码网络无监督维数约简[J].智能系统学报,2018,13(05):808.[doi:10.11992/tis.201804051]
 YANG Wenyuan.Unsupervised dimensionality reduction of multi-label learning via autoencoder networks[J].CAAI Transactions on Intelligent Systems,2018,13(01):808.[doi:10.11992/tis.201804051]

备注/Memo

备注/Memo:
收稿日期:2006-03-01.
基金项目:国家自然科学基金资助项目(60332010,60533030).
作者简介:
徐     蓉,女,1982年生,哈尔滨工业大学在读硕士研究生,主要研究方向为模式识别、机器学习、手语识别.
姜     峰,在职博士研究生,讲师.主要研究方向为模式识别、机器学习、自然人机交互技术、多媒体技术、数字版权保护等.
姚鸿勋,教授,博导.主要研究方向为自然人机交互技术、多媒体技术、图像处理及模式识别、信息隐藏与检测、数字版权保护、生物特征识别技术等.已发表学术论文60余篇,其中被SCI、EI、 ISTP检索收录30余篇,另获发明专利1项.
更新日期/Last Update: 2009-04-07