Locally linear embedding: A survey

Artificial Intelligence Review

Volumn 36, Issue 1, 2011, Pages 29-48

  Chen, Jing ^a   Liu, Yang ^a  

^a GUANGDONG UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Locally linear embedding; Nonlinear dimensionality reduction

Indexed keywords

EIGEN-PROBLEMS; EMBEDDINGS; HIGH DIMENSIONAL DATA; ILL-CONDITIONED; LOCALLY LINEAR EMBEDDING; NON-ITERATIVE; NONLINEAR DIMENSIONAL REDUCTION; NONLINEAR DIMENSIONALITY REDUCTION;

CLUSTERING ALGORITHMS;

EID: 79956087493     PISSN: 02692821     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10462-010-9200-z     Document Type: Article

References (69)

1. M Balasubramanian EL Schwartz JB Tenenbaum V de Silva JC Langford 2002 The isomap algorithm and topological stability Science 295 7 10.1126/science.295.5552.7a
2. Beckmann N, Kriegel HP, Schneider R, Seeger B (1990) The R*-tree: an efficient and robust access method for points and rectangles. In: Proceedings of the 1990 ACM SIGMOD international conference on Management of data, pp 322-331
3. PN Belhumeur JP Hespanha DJ Kriegman 1997 Eigenfaces vs. Fisherfaces: recognition using class specific linear IEEE T Pattern Anal 19 711 720 10.1109/34.598228 (Pubitemid 127762263)
4. M Belkin P Niyogi 2003 Laplacian eigenmaps for dimensionality reduction and Laplacian eigenmaps for dimensionality reduction and data representation Neural Comput 15 6 1373 1396 1085.68119 10.1162/089976603321780317 (Pubitemid 37049796)
5. Bengio Y, Paiement J, Vincent P, Delalleau O, Roux NL, Ouimet M (2003) Out-of-sample extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral clustering. In: Advances in neural information processing systems, pp 177-184
6. Brand M (2003) Charting a manifold. In: Advances in neural information processing systems, vol 15, pp 961-968
7. Cai D (2009) Spectral regression: a regression framework for efficient regularized subspace learning, UIUC
8. Cai D, He X, Han J (2007) Spectral regression for efficient regularized subspace learning. ICCV, pp 1-8
9. H Chang D Yeung 2006 Robust locally linear embedding Pattern Recognit 39 6 1053 1065 1096.68713 10.1016/j.patcog.2005.07.011
10. F de La Torre MJ Black 2003 A framework for robust subspace learning Int J Computer Vision 54 1-3 117 142 1076.68058 10.1023/A:1023709501986
11. de Ridder D, Kouropteva O, Okun, Oleg (2003) Supervised locally linear embedding. In: Proceedings of ICANN, pp 333-341
12. D Donoho C Grimes 2003 Hessian eigenmaps: new tools for nonlinear dimensionality reduction Proc Natl Acad Sci 100 5591 5596 1981019 1130.62337 10.1073/pnas.1031596100 (Pubitemid 36576852)
13. Eftekhari A, Abrishami-Moghaddam H, Babaie-Zadeh M (2009a) k/K-Nearest neighborhood criterion for improvement of locally linear embedding. CAIP, pp 808-815
14. Eftekhari A, Babaie-Zadeh M, Jutten C, Moghaddam HA (2009b) Robust-SL0 for stable sparse representation in noisy settings. ICASSP, pp 3433-3436
15. Fienberq S (1985) The analysis of crossclassified categorical data. MIT press, Cambridge
16. Goldberg Y, Ritov Y (2008) LDR-LLE: LLE with low-dimensional neighborhood representation. ISVC, pp 43-54
17. Guihua W, Lijun J, Jun W (2008) Kernel relative transformation with applications to enhancing locally linear embedding. IJCNN, pp 3401-3406
18. Hadid A, Pietikainen M (2003) Efficient locally linear embeddings of imperfect manifolds. MLDM, pp 188-201 (Pubitemid 36904955)
19. Han PY, Beng Jin AT, Kiong WE (2008) Neighbourhood discriminant locally linear embedding in face recognition. CGIV2008, pp 223-228
20. X He D Cai S Yan H Zhang 2005 Neighborhood preserving embedding IEEE Int Conf Comput Vis 2 1208 1213 (Pubitemid 44042318)
21. Holland PW, Welsch RE (1977) Communications in statistics: theory and methods
22. C Hou J Wang Y Wu D Yi 2009 Local linear transformation embedding Neurocomputing 72 10-12 2368 2378 10.1016/j.neucom.2008.12.002
23. C Hou C Zhang Y Wu Y Jiao 2009 Stable local dimensionality reduction approaches Pattern Recognit 42 9 2054 2066 1177.68171 10.1016/j.patcog.2008.12. 009
24. Hui K, Wang C (2008) Clustering-based locally linear embedding. ICPR
25. S Kadoury MD Levine 2007 Face detection in gray scale images using locally linear embeddings Comput Vis Image Underst 105 1 1 20 10.1016/j.cviu.2006.06.009 (Pubitemid 46014618)
26. R Karbauskaite O Kurasova G Dzemyda 2007 Selection of the number of neighbors of each data point for the locally linear embedding algorithm Inf Technol Control 36 4 359 364
27. Kouropteva O, Okun O, inen MPA (2002) Selection of the optimal parameter value for the locally linear embedding algorithm. In: Proceedings of the 1st international conference on fuzzy systems and knowledge discovery, pp 359-363
28. O Kouropteva O Okun M Pietikäinen 2005 Incremental locally linear embedding Pattern Recognit 38 10 1764 1767 1077.68800 10.1016/j.patcog.2005.04. 006 (Pubitemid 41037108)
29. B Li C Zheng D Huang 2008 Locally linear discriminant embedding: an efficient method for face recognition Pattern Recognit 41 12 3813 3821 1173.68673 10.1016/j.patcog.2008.05.027
30. H Li T Jiang K Zhang 2006 Efficient and robust feature extraction by maximum margin criterion IEEE Trans Neural Netw 17 1 157 165 10.1109/TNN.2005.860852 (Pubitemid 43263948)
31. SZ Li J Lu 1999 Face recognition using the nearest feature line method IEEE Trans Neural Netw 10 4 439 443 10.1109/72.750575
32. Lingzhu H, Lingxiang Z, Caiyue C, Min L (2009) Locally linear embedding algorithm with adaptive neighbors. ISA
33. Y Pan SS Ge A Al Mamun 2009 Weighted locally linear embedding for dimension reduction Pattern Recognitn 42 5 798 811 1178.68453 10.1016/j.patcog.2008.08.024
34. Pang YH, Teoh ABJ, Wong EK, Abas FS (2008) Supervised locally linear embedding in face recognition. ISBAST'08.
35. Park J, Zhang Z, Zha H, Kasturi R (2004) Local smoothing for manifold learning. CVPR I452-I459
36. P Qiu 2004 The local piecewisely linear kernel smoothing procedure for fitting jump regression surfaces Technometrics 46 87 98 2043390 10.1198/004017004000000149
37. ST Roweis LK Saul 2000 Nonlinear dimensionality reduction by locally linear embedding Science 290 5500 2323 2326 10.1126/science.290.5500.2323 (Pubitemid 32041578)
38. LK Saul ST Rowels 2004 Think globally, fit locally: unsupervised learning of low dimensional manifolds J Mach Learn Res 4 2 119 155 2050880 1093.68089 10.1162/153244304322972667
39. JB Tenenbaum V De Silva JC Langford 2000 A global geometric framework for nonlinear dimension reduction Science 290 5500 2319 2323 10.1126/science.290. 5500.2319 (Pubitemid 32041577)
40. Teng X, Wu B, Yu W, Liu C, (2005) A hand gesture recognition system based on local linear embedding J Visual Lang & Computing Special issue section on Context and Emotion Aware Visual Interaction - Part I 16(5): 442-454 (Pubitemid 41294374)
41. Tikhonov AN (1963) Regularization of incorrectly posed problems
42. Valencia-Aguirre J, Álvarez-Mesa A, Daza-Santacoloma G, Castellanos-Domínguez G (2009) Automatic choice of the number of nearest neighbors in locally linear embedding CIARP2009, pp 77-84
43. C Varini A Degenhard TW Nattkemper 2006 ISOLLE: LLE with geodesic distance Neurocomputing 69 13-15 1768 1771 10.1016/j.neucom.2005.12.120 (Pubitemid 43906072)
44. Wang H, Zheng J, Yao Z, Li L (2006) Improved locally linear embedding through new distance computing. ISNN, pp 1326-1333 (Pubitemid 44046274)
45. Wang J (2008) Robust and stable locally linear embedding. FSKD, pp 197-201
46. J Wang Z Zhang 2010 Nonlinear embedding preserving multiple local-linearities Pattern Recognit 43 4 1257 1268 1192.68615 10.1016/j.patcog.2009.09.014
47. Y Wang Y Wu 2010 Complete neighborhood preserving embedding for face recognition Pattern Recognit 43 3 1008 1015 1187.68512 10.1016/j.patcog.2009.08. 009
48. DJ Watts SH Strogatz 1998 Collective dynamics of small-world networks Nature 393 6684 440 442 10.1038/30918 (Pubitemid 28292183)
49. KQ Weinberger LK Saul 2006 Unsupervised learning of image manifolds by semidefinite programming Int J Comput Vis 70 1 77 90 10.1007/s11263-005-4939-z (Pubitemid 43855868)
50. Wen G, Jiang L (2006) Clustering-based locally linear embedding. In: Proceedings of 2006 IEEE international conference on systems, man and cybernetics pp 4192-4196 (Pubitemid 47297737)
51. Wen G, Jiang L, Wen J, Shadbolt NR (2006) Performing locally linear embedding with adaptable neighborhood size on manifold. J Softw, pp 985-989 (Pubitemid 44531896)
52. F Wu ZY Hu 2006 The LLE and a linear mapping Pattern Recognit 39 9 1799 1804 1110.68167 10.1016/j.patcog.2006.03.019 (Pubitemid 43867578)
53. Xia T, Li J, Zhang Y, Tang S (2008) A more topologically stable locally linear embedding algorithm based on R*-tree. PAKDD, pp 803-812 (Pubitemid 351776373)
54. Y Yan Y Zhang 2008 Discriminant projection embedding for face and palmprint recognition Neurocomputing 71 16-18 3534 3543 10.1016/j.neucom.2007. 09.013
55. J Yin D Hu Z Zhou 2008 Noisy manifold learning using neighborhood smoothing embedding Pattern Recognit Lett 29 11 1613 1620 10.1016/j.patrec.2008. 04.002
56. HP Ying BJ Andrew Teoh EK Wong 2008 Neighbourhood discriminant embedding in face recognition IEICE Electron Express 5 24 1036 1041 10.1587/elex.5.1036
57. Yulin Z, Jian Z, Sun'an W, Xiaohu L (2008) Local linear embedding in dimensionality reduction based on small world principle. CSSE, pp 394-398
58. Zeng X, Luo S (2008) Generalized locally linear embedding based on local reconstruction similarity. FSKD2008, pp 305-309
59. Zhan D, Zhou Z (2006) Neighbor line-based locally linear embedding. PAKDD, pp 806-815 (Pubitemid 44019487)
60. C Zhang J Wang N Zhao D Zhang 2004 Reconstruction and analysis of multi-pose face images based on nonlinear dimensionality reduction Pattern Recognit 37 2 325 336 2082752 1059.68124 10.1016/j.patcog.2003.07.005 (Pubitemid 37436241)
61. S Zhang 2009 Enhanced supervised locally linear embedding Pattern Recognit Lett 30 13 1208 1218 10.1016/j.patrec.2009.05.011
62. Z Zhang J Wang 2007 MLLE: modified locally linear embedding using multiple weights Adv Neural Inf Process Syst 19 1593 1600
63. Zhang X, Liu Y, Gao C, Liu J (2008) An efficient algorithm of learning the parametric map of locally linear embedding. IITA, pp 52-56
64. Z Zhang H Zha 2005 Principal manifolds and nonlinear dimensionality reduction via tangent space alignment SIAM J Sci Comput 26 1 313 338 2114346 10.1137/S1064827502419154 (Pubitemid 40297703)
65. Zhang Z, Zhao L (2007) Probability-based locally linear embedding for classification. FSKD, pp 243-247 (Pubitemid 351710897)
66. D Zhao 2006 Formulating LLE using alignment technique Pattern Recognit 39 2233 2235 1102.68644 10.1016/j.patcog.2006.05.007 (Pubitemid 44175455)
67. L Zhao Z Zhang 2009 Supervised locally linear embedding with probability-based distance for classification Comput Math Appl 57 6 919 926 1186.68401 10.1016/j.camwa.2008.10.055
68. Zhao Q, Zhang D, Lu H (2005) Supervised LLE in ICA space for facial expression recognition. ICNNB'05, pp 1970-1975 (Pubitemid 46289316)
69. CY Zhou YQ Chen 2006 Improving nearest neighbor classification with cam weighted distance Pattern Recognit 39 4 635 645 1122.68576 10.1016/j.patcog. 2005.09.004 (Pubitemid 43204309)