第5期 文贵华，等：局部测地距离估计的Hessian局部线性嵌入 ·435· [2]ROW EIS S T,SAUL L K Nonlinear dmensionality reduc- bedd ing based on opti ization of neighborhood [J].Joumal tion by locally linear embedding [J]Science,2000,290 of System Smulaton,2007,19(13):3119-3122 (12):2319-2323 [15 ]W EN Guihua,J ANGLijun,NIGEL R S Using graph al [3 ]BELKN M,NIYOGI P Laplacian eigermaps for dmen- gebra to optm ize neighborhood for Isometric mapping sionality reduction and data representation[J Neural Com- [C]//20th Intemational Joint Conference on Artificial In- puting.2003,15(6):1373-1396 telligence DCA 1-07).India,2007:2398-2403. 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[19]De R DDER D,LOOGM,RENDERS M J T Local fisher [8 ]CHANG Hong.YENG Dityan Robust bcally linear embed- embedding [C]//Proceedings of the 17th Intemational ding[J].Pattem Recognition,2000,39(6):1053-1065. Conference on Pattem Recognition Cambridge,UK, [9]YANGL.Building k-connected neighborhood graphs for iso- 2004:295298 metric data embedding[J].EEE Transactions on Pattem A- [20 ]HONG Chang,YEUND Yang Robust locally linear em- nalysis and Machine Intelligence,2006,28(5):827-831. bedding[J ]Pattem Recognition,2003,39(6):1053- [10]YANG L Building connected neighborhood graphs for 1065 cally linear embedding[C]//18 th Intemational Conference 作者简介： on Pattem Recognition Hong Kong,China,2006:1680- 文贵华，男，1968年生，主要研究方向 1683 为创新计算、认知几何、机器学习与数据挖 [11 ]VAR NI C,DEGENHARD A,NATTKEMPER T W. SOLLE:LLE with geodesic distance[J].Neurocomputing. 2006,69(15):1768-1771 [12王和勇，郑杰，姚正安，李磊.基于聚类和改进距离 的LE方法在数据降维中的应用[J]计算机研究与发 江丽君，女，1971年生，主要研究方向 展，2006.43(8)：1485-1490 为机器学习与图形CAD WANG Heyong,ZHENG Jie,YAO Zhengan,LILei Ap- plication of diension reduction on using mproved LLE based on clustering[J].Joumal of Computer Research and Development,.2006,43(8):1485-1490 文军，男，1964年生，主要研究方向 [13]WEN Guihua,JANG Lijun,WEN Jun,NIGEL R S 为创新计算与应用。 Clustering-based nonlinear dmensionality reduction on manifold [C ]//Lecture Notes in Artificial Intelligence (LNA D).Springer,2006:444-453. [14文贵华江丽君，文军.基于邻域优化的局部线性嵌入 [J]系统仿真学报，2007,19(13)：3119-3122 WEN Guihua,JANGLijun,WEN Jun Locally linear em- 1994-2009 China Academic Journal Electronic Publishing House.All rights reserved.http://www.cnki.net[ 2 ]ROW EIS S T, SAUL L K. Nonlinear dimensionality reduc2 tion by locally linear embedding [ J ]. Science, 2000, 290 (12) : 231922323. [ 3 ]BELKIN M, N IYOGI P. Lap lacian eigenmap s for dimen2 sionality reduction and data rep resentation [J ]. Neural Com2 puting, 2003, 15 (6) : 137321396. [ 4 ] DONOHO D L, GR IMES C. Hessian eigenmap s: locally linear embedding, techniques for high2dimensional data[J ]. PNAS, 2003, 100 (10) : 5912596. [ 5 ]De R IDDER D, KOUROPTEVA O, OKUN O, et al. Super2 vised locally linear embedding [ C ] / /A rtificial Neural Net2 works and Neural Information Processing. Istanbul, Turkey: Sp ringer, 2003: 3332341. [ 6 ] KOUROPTEVA O, OKUN O, P IETIKA INEN M. Incremen2 tal locally linear embedding[J ]. Pattern Recognition, 2005, 38 (10) : 1764217671 [ 7 ]De R IDDER D, LOOGM, REINDERSM J T. Local fisher embedding[C ] / /Proceedings of the 17 th International Con2 ference on Pattern Recognition. [ S. l. ], 2004: 29522981 [ 8 ]CHANG Hong, YENG D ityan. Robust locally linear embed2 ding[J ]. Pattern Recognition, 2000, 39 (6) : 105321065. [ 9 ] YANG L. Building k2connected neighborhood graphs for iso2 metric data embedding[J ]. IEEE Transactions on Pattern A2 nalysis and Machine Intelligence, 2006, 28 (5) : 8272831. [ 10 ]YANG L. Building connected neighborhood graphs for lo2 cally linear embedding[ C ] / /18 th International Conference on Pattern Recognition. Hong Kong, China, 2006: 16802 1683. [ 11 ] VAR IN I C, DEGENHARD A, NATTKEMPER T W. ISOLLE: LLE with geodesic distance[J ]. Neurocomputing, 2006, 69 (15) : 176821771. [ 12 ]王和勇 ,郑 杰 ,姚正安 ,李 磊. 基于聚类和改进距离 的 LLE方法在数据降维中的应用 [J ]. 计算机研究与发 展 , 2006, 43 (8) : 148521490. WANG Heyong, ZHENG Jie, YAO Zhengan, L ILei. Ap2 p lication of dimension reduction on using imp roved LLE based on clustering[J ]. Journal of Computer Research and Development, 2006, 43 (8) : 148521490. [ 13 ]W EN Guihua, J IANG L ijun, W EN Jun, N IGEL R S. Clustering2based nonlinear dimensionality reduction on manifold [ C ] / /Lecture Notes in A rtificial Intelligence (LNA I). Sp ringer, 2006: 4442453. [ 14 ]文贵华、江丽君 ,文 军. 基于邻域优化的局部线性嵌入 [J ]. 系统仿真学报 , 2007, 19 (13) : 311923122. W EN Guihua, J IANG L ijun, W EN Jun. Locally linear em2 bedding based on op tim ization of neighborhood [J ]. Journal of System Simulation, 2007, 19 (13) : 311923122. [ 15 ]W EN Guihua, J IANGL ijun , N IGEL R S. U sing graph al2 gebra to op timize neighborhood for Isometric mapp ing [C ] / /20 th International Joint Conference on A rtificial In2 telligence ( IJCA I207). India, 2007: 239822403. [ 16 ] SAMKO O, MARSHALL A D, ROSIN P L. Selection of the op timal parameter value for the Isomap algorithm [J ]. Pattern Recognition Letters, 2006, 27 (9) : 9682979. [ 17 ]文贵华 ,江丽君 ,文 军. 邻域参数动态变化的局部线性 嵌入 [J ]. 软件学报 , 2008, 19 (7) : 166621673. W EN Guihua, J IANG L ijun, W EN Jun. Dynam ically deter2 m ining neighborhood parameter for locally linear embedding [J ]. Journal of Software, 2008, 19 (7) : 166621673. [ 18 ]W EN Guihua, J IANG L ijun. Globalizing local neighbor2 hood for locally linear embedding [ C ] / /Proceedings of 2006 IEEE International Conference on System, Man and Cybernetics. Taibei, China, 2006: 349123496. [ 19 ]De R IDDER D,LOOG M, REINDERS M J T. Local fisher embedding [ C ] / /Proceedings of the 17 th International Conference on Pattern Recognition. Cambridge, UK, 2004: 2952298. [ 20 ] HONG Chang, YEUND Yang. Robust locally linear em2 bedding[ J ]. Pattern Recognition, 2003, 39 ( 6 ) : 10532 1065. 作者简介 : 文贵华 , 男 , 1968年生 ,主要研究方向 为创新计算、认知几何、机器学习与数据挖 掘. 江丽君 , 女 , 1971年生 ,主要研究方向 为机器学习与图形 CAD. 文 军 , 男 , 1964年生 ,主要研究方向 为创新计算与应用. 第 5期 文贵华 ,等 :局部测地距离估计的 Hessian局部线性嵌入 ·435·