A survey of multilinear subspace learning for tensor data

Pattern Recognition

Volumn 44, Issue 7, 2011, Pages 1540-1551

  Lu, Haiping ^a   Plataniotis, Konstantinos N ^b   Venetsanopoulos, Anastasios N ^b,c  

^a INSTITUTE FOR INFOCOMM RESEARCH   (Singapore)

^b UNIVERSITY OF TORONTO   (Canada)

^c RYERSON UNIVERSITY   (Canada)

Author keywords

Dimensionality reduction; Feature extraction; Multidimensional data; Multilinear; Subspace learning; Survey; Taxonomy; Tensor

Indexed keywords

ALGORITHMIC ASPECTS; DIMENSIONALITY REDUCTION; FUTURE RESEARCH DIRECTIONS; MASSIVE DATA; MULTIDIMENSIONAL DATA; MULTILINEAR; MULTILINEAR PROJECTION; STRONG DEMAND; SUBSPACE LEARNING;

FEATURE EXTRACTION; LEARNING ALGORITHMS; SURVEYS; TAXONOMIES; TENSORS;

DATA REDUCTION;

EID: 79952194000     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2011.01.004     Document Type: Article

References (113)

1. J. Ye, R. Janardan, Q. Li, GPCA: an efficient dimension reduction scheme for image compression and retrieval, in: The Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2004, pp. 354363. (Pubitemid 40114945)
2. S. Yan, D. Xu, Q. Yang, L. Zhang, X. Tang, and H. Zhang Multilinear discriminant analysis for face recognition IEEE Transactions on Image Processing 16 1 2007 212 220 (Pubitemid 46437483)
3. J. Lu, K.N. Plataniotis, and A.N. Venetsanopoulos Face recognition using kernel direct discriminant analysis algorithms IEEE Transactions on Neural Networks 14 1 2003 117 126
4. H. Lu, J. Wang, and K.N. Plataniotis A review on face and gait recognition: system, data and algorithms S. Stergiopoulos, Advanced Signal Processing Handbook second ed. 2009 CRC Press Boca Raton, Florida 303 330
5. J. Li, L. Zhang, D. Tao, H. Sun, and Q. Zhao A prior neurophysiologic knowledge free tensor-based scheme for single trial eeg classification IEEE Transactions on Neural Systems and Rehabilitation Engineering 17 2 2009 107 115
6. H. Lu, K.N. Plataniotis, A.N. Venetsanopoulos, Regularized common spatial patterns with generic learning for EEG signal classification, in: Proceedings of 31st International Conference of the IEEE Engineering in Medicine and Biology Society, 2009.
7. J. Ye, T. Li, T. Xiong, and R. Janardan Using uncorrelated discriminant analysis for tissue classification with gene expression data IEEE/ACM Transactions on Computational Biology Bioinformatics 1 4 2004 181 190 (Pubitemid 40325595)
8. H.S. Sahambi, and K. Khorasani A neural-network appearance-based 3-D object recognition using independent component analysis IEEE Transactions on Neural Networks 14 1 2003 138 149
9. N. Renard, and S. Bourennane Dimensionality reduction based on tensor modeling for classification methods IEEE Transactions on Geoscience and Remote Sensing 47 4 2009 1123 1131
10. R. Chellappa, A. Roy-Chowdhury, and S. Zhou Recognition of Humans and their Activities using Video 2005 Morgan & Claypool Publishers San Rafael, California
11. R.D. Green, and L. Guan Quantifying and recognizing human movement patterns from monocular video images-part II: applications to biometrics IEEE Transactions on Circuits and Systems for Video Technology 14 2 2004 191 198
12. D.R. Hardoon, and J. Shawe-Taylor Decomposing the tensor kernel support vector machine for neuroscience data with structure labels Machine Learning 79 12 2010 29 46
13. X. He, Incremental semi-supervised subspace learning for image retrieval, in: ACM Conference on Multimedia 2004, 2004, pp. 28. (Pubitemid 40211711)
14. E. Shechtman, Y. Caspi, and M. Irani Space-time super-resolution IEEE Transactions on Pattern Analysis and Machine Intelligence 27 4 2005 531 545 (Pubitemid 40556109)
15. J. Sun, D. Tao, C. Faloutsos, Beyond streams and graphs: dynamic tensor analysis, in: Proceedings the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2006, pp. 374383. (Pubitemid 44535534)
16. J. Sun, Y. Xie, H. Zhang, and C. Faloutsos Less is more: sparse graph mining with compact matrix decomposition Statistical Analysis and Data Mining 1 1 2008 6 22
17. J. Sun, D. Tao, S. Papadimitriou, P.S. Yu, and C. Faloutsos Incremental tensor analysis: theory and applications ACM Transactions on Knowledge Discovery from Data 2 3 2008 11:1 11:37
18. G. Shakhnarovich, and B. Moghaddam Face recognition in subspaces S.Z. Li, A.K. Jain, Handbook of Face Recognition 2004 Springer-Verlag 141 168
19. I.T. Jolliffe Principal Component Analysis second ed. 2002 Springer Series in Statistics
20. S.Z. Li, and A.K. Jain Introduction S.Z. Li, A.K. Jain, Handbook of Face Recognition 2004 Springer-Verlag 1 11
21. H. Lu, K.N. Plataniotis, and A.N. Venetsanopoulos MPCA: multilinear principal component analysis of tensor objects IEEE Transactions on Neural Networks 19 1 2008 18 39 (Pubitemid 351279223)
22. D. Tao, X. Li, X. Wu, W. Hu, and S.J. Maybank Supervised tensor learning Knowledge and Information Systems 13 1 2007 1 42
23. D. Tao, X. Li, X. Wu, and S.J. Maybank General tensor discriminant analysis and gabor features for gait recognition IEEE Transactions on Pattern Analysis and Machine Intelligence 29 10 2007 1700 1715
24. D. Tao, X. Li, X. Wu, and S.J. Maybank Tensor rank one discriminant analysis a convergent method for discriminative multilinear subspace selection Neurocomputing 71 1012 2008 1866 1882
25. H. Lu, K.N. Plataniotis, and A.N. Venetsanopoulos Uncorrelated multilinear principal component analysis for unsupervised multilinear subspace learning IEEE Transactions on Neural Networks 20 11 2009 1820 1836
26. H. Lu, K.N. Plataniotis, and A.N. Venetsanopoulos Uncorrelated multilinear discriminant analysis with regularization and aggregation for tensor object recognition IEEE Transactions on Neural Networks 20 1 2009 103 123
27. D. Xu, S. Yan, L. Zhang, S. Lin, H.-J. Zhang, and T.S. Huang Reconstruction and recognition of tensor-based objects with concurrent subspaces analysis IEEE Transactions on Circuits and Systems for Video Technology 18 1 2008 36 47
28. H. Lu, K.N. Plataniotis, and A.N. Venetsanopoulos A taxonomy of emerging multilinear discriminant analysis solutions for biometric signal recognition N.V. Boulgouris, K. Plataniotis, E. Micheli-Tzanakou, Biometrics: Theory, Methods, and Applications 2009 Wiley/IEEE 21 45
29. W.H. Greub Multilinear Algebra 1967 Springer-Verlag Berlin
30. L.D. Lathauwer, B.D. Moor, and J. Vandewalle A multilinear singular value decomposition SIAM Journal of Matrix Analysis and Applications 21 4 2000 1253 1278 (Pubitemid 33217068)
31. N) approximation of higher-order tensors SIAM Journal of Matrix Analysis and Applications 21 4 2000 1324 1342 (Pubitemid 33217072)
32. L. Qi, W. Sun, and Y. Wang Numerical multilinear algebra and its applications Frontiers of Mathematics in China 2 4 2007 501 526
33. D. Muti, and S. Bourennane Survey on tensor signal algebraic filtering Signal Processing 87 2 2007 237 249 (Pubitemid 44602251)
34. E. Acar, and B. Yener Unsupervised multiway data analysis: a literature survey IEEE Transactions on Knowledge and Data Engineering 21 1 2009 6 20
35. T.G. Kolda, and B.W. Bader Tensor decompositions and applications SIAM Review 51 3 2009 455 500
36. S. Zafeiriou Algorithms for nonnegative tensor factorization S. Aja-Fernndez, R.d.L. Garca, D. Tao, X. Li, Tensors in Image Processing and Computer Vision 2009 Springer 105 124
37. T. Hazan, S. Polak, A. Shashua, Sparse image coding using a 3D non-negative tensor factorization, in: Proceedings of IEEE Conference on Computer Vision, vol. 1, 2005, pp. 5057. (Pubitemid 44054940)
38. A. Shashua, T. Hazan, Non-negative tensor factorization with applications to statistics and computer vision, in: Proceedings of International Conference on Machine Learning, 2005, pp. 792799.
39. R. Bro, Multi-way analysis in the food industry models, algorithms and applications, Ph.D. Thesis, University of Amsterdam, The Netherlands. URL 〈 http://www.models.kvl.dk/sites/default/files/brothesis-0.pdf 〉, 1998.
40. A.K. Smilde, R. Bro, and P. Geladi Multi-way Analysis 2004 John Wiley and Sons
41. B.W. Bader, and T.G. Kolda Algorithm 862: Matlab tensor classes for fast algorithm prototyping ACM Transactions on Mathematical Software 32 4 2006 635 653 (Pubitemid 44927149)
42. H. Lu, Multilinear subspace learning for face and gait recognition, Ph.D. Thesis, University of Toronto, 2008. URL 〈 https://tspace.library. utoronto.ca/handle/1807/16750 〉.
43. X. He, D. Cai, P. Niyogi, Tensor subspace analysis, in: Advances in Neural Information Processing Systems 18 (NIPS), 2005.
44. R.O. Duda, P.E. Hart, and D.G. Stork Pattern Classification second ed. 2001 Wiley Interscience
45. T.K. Moon, and W.C. Stirling Mathematical Methods and Algorithms for Signal Processing 2000 Prentice Hall
46. Y. Wang, S. Gong, Tensor discriminant analysis for view-based object recognition, in: Proceedings of International Conference on Pattern Recognition, vol. 3, 2006, pp. 3336. (Pubitemid 46553059)
47. D. Tao, X. Li, X. Wu, S.J. Maybank, Elapsed time in human gait recognition: a new approach, in: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 2, 2006, pp. 177180.
48. G. Hua, P.A. Viola, S.M. Drucker, Face recognition using discriminatively trained orthogonal rank one tensor projections, in: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2007, pp. 18.
49. M. Turk, and A. Pentland Eigenfaces for recognition Journal of Cognitive Neurosicence 3 1 1991 71 86
50. P.N. Belhumeur, J.P. Hespanha, and D.J. Kriegman Eigenfaces vs. fisherfaces: recognition using class specific linear projection IEEE Transactions on Pattern Analysis and Machine Intelligence 19 7 1997 711 720 (Pubitemid 127762263)
51. P. Comon Independent component analysis a new concept? Signal Processing 36 1994 287 314
52. B. Thompson Canonical Correlation Analysis: Uses and Interpretation 1984 Sage Publications Thousand Oaks, CA
53. J.D. Carroll, and J.J. Chang Analysis of individual differences in multidimensional scaling via an n-way generalization of "eckart-young" decomposition Psychometrika 35 1970 283 319
54. R.A. Harshman Foundations of the parafac procedure: models and conditions for an "explanatory" multi-modal factor analysis UCLA Working Papers in Phonetics 16 1970 1 84
55. P. Kroonenberg, and J. Leeuw Principal component analysis of three-mode data by means of alternating least squares algorithms Psychometrika 45 1 1980 69 97
56. J. Yang, D. Zhang, A.F. Frangi, and J. Yang Two-dimensional PCA: a new approach to appearance-based face representation and recognition IEEE Transactions on Pattern Analysis and Machine Intelligence 26 1 2004 131 137
57. J. Ye Generalized low rank approximations of matrices Machine Learning 61 13 2005 167 191 (Pubitemid 43049367)
58. H. Wang, and N. Ahuja A tensor approximation approach to dimensionality reduction International Journal of Computer Vision 76 3 2008 217 229
59. D. Tao, M. Song, X. Li, J. Shen, J. Sun, X. Wu, C. Faloutsos, and S.J. Maybank Bayesian tensor approach for 3-D face modeling IEEE Transactions on Circuits and Systems for Video Technology 18 10 2008 1397 1410
60. C.M. Bishop, Bayesian PCA, in: Advances in Neural Information Processing Systems (NIPS), 1999, pp. 382388.
61. K. Inoue, K. Hara, K. Urahama, Robust multilinear principal component analysis, in: Proceedings of IEEE Conference on Computer Vision, 2009, pp. 591597.
62. Y. Panagakis, C. Kotropoulos, and G.R. Arce Non-negative multilinear principal component analysis of auditory temporal modulations for music genre classification IEEE Transactions on Audio, Speech, and Language Processing 18 3 2010 576 588
63. S. Papadimitriou, J. Sun, C. Faloutsos, Streaming pattern discovery in multiple time-series, in: Proceedings of 31st International Conference on Very Large Data Bases, 2005, pp. 697708. (Pubitemid 43991045)
64. A. Shashua, A. Levin, Linear image coding for regression and classification using the tensor-rank principle, in: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, vol. I, 2001, pp. 4249.
65. J. Ye, R. Janardan, Q. Li, Two-dimensional linear discriminant analysis, in: Advances in Neural Information Processing Systems (NIPS), 2004, pp. 15691576.
66. Q. Liu, X. Tang, H. Lu, and S. Ma Face recognition using kernel scatter-difference-based discriminant analysis IEEE Transactions on Neural Networks 17 4 2006 1081 1085 (Pubitemid 44194165)
67. K. Fukunaga Introduction to Statistical Pattern Recognition 1990 Academic Press Boston, MA
68. T.G. Kolda Orthogonal tensor decompositions SIAM Journal of Matrix Analysis and Applications 23 1 2001 243 255
69. Z. Jin, J.Y. Yang, Z.M. Tang, and Z.S. Hu A theorem on the uncorrelated optimal discriminant vectors Pattern Recognition 34 10 2001 2041 2047 (Pubitemid 32760633)
70. J. Ye, R. Janardan, Q. Li, and H. Park Feature reduction via generalized uncorrelated linear discriminant analysis IEEE Transactions on Knowledge and Data Engineering 18 10 2006 1312 1322 (Pubitemid 44335197)
71. L.R. Tucker Some mathematical notes on three-mode factor analysis Psychometrika 31 1966 279 311
72. A. Kapteyn, H. Neudecker, and T. Wansbeek An approach to n-mode components analysis Psychometrika 51 1986 269 275
73. J.D. Carroll, S. Pruzansky, and J.B. Kruskal CANDELINC: a general approach to multidimensional analysis of many-way arrays with linear constraints on parameters Psychometrika 45 1980 3 24
74. P. Comon, and B. Mourrain Decomposition of quantics in sums of powers of linear forms Signal Processing 53 1996 93 108
75. N) reduction in multilinear algebra Linear Algebra and its Applications 391 2004 31 55
76. M.A.O. Vasilescu, D. Terzopoulos, Multilinear analysis of image ensembles: tensorfaces, in: Proceedings of Seventh European Conference on Computer Vision, 2002, pp. 447460.
77. M.A.O. Vasilescu, D. Terzopoulos, Multilinear image analysis for facial recognition, in: Proceedings of International Conference on Pattern Recognition, vol. 2, 2002, pp. 511514. (Pubitemid 44844789)
78. M.A.O. Vasilescu, Human motion signatures: analysis, synthesis, recognition, in: Proceedings of International Conference on Pattern Recognition, vol. 3, 2002, pp. 456460. (Pubitemid 44844525)
79. C.S. Lee, A. Elgammal, Towards scalable view-invariant gait recognition: Multilinear analysis for gait, in: Proceedings of International Conference on Audio and Video-Based Biometric Person Authentication, 2005, pp. 395405. (Pubitemid 41423056)
80. T.-K. Kim, and R. Cipolla Canonical correlation analysis of video volume tensors for action categorization and detection IEEE Transactions on Pattern Analysis and Machine Intelligence 31 8 2009 1415 1428
81. D. Xu, S. Yan, S. Lin, T.S. Huang, and S.-F. Chang Enhancing bilinear subspace learning by element rearrangement IEEE Transactions on Pattern Analysis and Machine Intelligence 31 10 2009 1913 1920
82. S. Yan, D. Xu, S. Lin, T.S. Huang, S.-F. Chang, Element rearrangement for tensor-based subspace learning, in: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2007, pp. 18.
83. J. Zhang, J. Pu, C. Chen, and R. Fleischer Low-resolution gait recognition IEEE Transactions on Systems, Man, and CyberneticsPart B: Cybernetics 40 4 2010 986 996
84. G. Dai, D.Y. Yeung, Tensor embedding methods, in: Proceedings of Twenty-First National Conference on Artificial Intelligence, 2006, pp. 330335. (Pubitemid 44705306)
85. S. Yan, D. Xu, B. Zhang, H.J. Zhang, Q. Yang, and S. Lin Graph embedding and extensions: a general framework for dimensionality reduction IEEE Transactions on Pattern Analysis and Machine Intelligence 29 1 2007 40 51 (Pubitemid 46415944)
86. D. Xu, S. Lin, S. Yan, and X. Tang Rank-one projections with adaptive margins for face recognition IEEE Transactions on Systems, Man, and CyberneticsPart B: Cybernetics 37 5 2007 1226 1236 (Pubitemid 47541886)
87. X. Gao, X. Li, J. Feng, and D. Tao Shot-based video retrieval with optical flow tensor and HMMs Pattern Recognition Letters 30 2 2010 140 147
88. S. Aja-Fernndez, R.d.L. Garca, D. Tao, X. Li (Eds.), Tensors in Image Processing and Computer Vision, Springer, 2009.
89. A. Cichocki, R. Zdunek, A.H. Phan, and S. Amari Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation 2009 Wiley-Blackwell
90. Workshop on Algorithms for Modern Massive Data Sets, 2010, 2008, 2006. URL 〈 http://www.stanford.edu/group/mmds/ 〉.
91. A.K. Jain, A. Ross, and S. Prabhakar An introduction to biometric recognition IEEE Transactions on Circuits and Systems for Video Technology 14 1 2004 4 20
92. J. Wang, A. Barreto, L. Wang, Y. Chen, N. Rishe, J. Andrian, and M. Adjouadi Multilinear principal component analysis for face recognition with fewer features Neurocomputing 73 1012 2010 1550 1555
93. H. Lu, K.N. Plataniotis, A.N. Venetsanopoulos, Uncorrelated multilinear principal component analysis through successive variance maximization, in: Proceedings of International Conference on Machine Learning, 2008, pp. 616623.
94. H. Lu, K.N. Plataniotis, A.N. Venetsanopoulos, Uncorrelated multilinear discriminant analysis with regularization for gait recognition, in: Proceedings of Biometrics Symposium 2007, 2007, doi: 10.1109/BCC.2007.4430540.
95. H. Lu, K.N. Plataniotis, A.N. Venetsanopoulos, Boosting LDA with regularization on MPCA features for gait recognition, in: Proceedings of Biometrics Symposium 2007, 2007, doi: 10.1109/BCC.2007.4430542.
96. H. Lu, K.N. Plataniotis, A.N. Venetsanopoulos, Multilinear principal component analysis of tensor objects for recognition, in: Proceedings of International Conference on Pattern Recognition, vol. 2, 2006, pp. 776779. (Pubitemid 46532314)
97. H. Lu, K.N. Plataniotis, and A.N. Venetsanopoulos Boosting discriminant learners for gait recognition using mpca features EURASIP Journal on Image and Video Processing 2009 11 10.1155/2009/713183 article ID 713183
98. B. Blankertz, R. Tomioka, S. Lemm, M. Kawanabe, and K.-R. Mller Optimizing spatial filters for robust EEG single-trial analysis IEEE Signal Processing Magazine 25 1 2008 41 56
99. J. Wen, X. Gao, Y. Yuan, D. Tao, and J. Li Incremental tensor biased discriminant analysis: a new color-based visual tracking method Neurocomputing 73 46 2010 827 839
100. H. Lu, H.-L. Eng, M. Thida, K.N. Plataniotis, Visualization and clustering of crowd video content in mpca subspace, in: Proceedings of 19th ACM Conference on Information and Knowledge Management, 2010, pp. 17771780.
101. X. Gao, Y. Yang, D. Tao, and X. Li Discriminative optical flow tensor for video semantic analysis Computer Vision and Image Understanding 113 3 2009 372 383
102. J. Wen, X. Li, X. Gao, D. Tao, Incremental learning of weighted tensor subspace for visual tracking, in: Proceedings of 2009 IEEE International Conference on Systems, Man and Cybernetics, 2009, pp. 36883693.
103. J.A. Ruiz-Hernandez, J.L. Crowley, A. Lux, "How old are you?": age estimation with tensors of binary gaussian receptive maps, in: Proceedings of the British Machine Vision Conference, 2010, pp. 6.111.
104. J.B. Tenenbaum, V. de Silva, and J. Langford A global geometric framework for nonlinear dimensionality reduction Science 290 22 2000 2319 2323 (Pubitemid 32041577)
105. S. Roweis, and L. Saul Nonlinear dimensionality reduction by locally linear embedding Science 290 22 2000 2323 2326 (Pubitemid 32041578)
106. X. He, S. Yan, Y. Hu, P. Niyogi, and H. Zhang Face recognition using Laplacianfaces IEEE Transactions on Pattern Analysis and Machine Intelligence 27 3 2005 328 340 (Pubitemid 40377326)
107. D. Cai, X. He, J. Han, and H.J. Zhang Orthogonal Laplacianfaces for face recognition IEEE Transactions on Image Processing 15 11 2006 3608 3614 (Pubitemid 44615155)
108. K.W. Bowyer, K. Chang, and P. Flynn A survey of approaches and challenges in 3D and multi-modal 3D 2D face recognition Computer Vision and Image Understanding 101 1 2006 1 15 (Pubitemid 41642085)
109. S.Z. Li, C. Zhao, M. Ao, Z. Lei, Learning to fuse 3D2D based face recognition at both feature and decision levels, in: Proceedings IEEE International Workshop on Analysis and Modeling of Faces and Gestures, 2005, pp. 4353.
110. A. Colombo, C. Cusano, and R. Schettini 3D face detection using curvature analysis Pattern Recognition 39 3 2006 444 455 (Pubitemid 41808625)
111. P.J. Phillips, P. Flynn, T. Scruggs, K. Bowyer, J. Chang, K. Hoffman, J. Marques, J. Min, W. Worek, Overview of the face recognition grand challenge, in: Proceedings IEEE Conference on Computer Vision and Pattern Recognition, vol. 1, 2005, pp. 947954. (Pubitemid 43897294)
112. R. Xu, and D.W. II Survey of clustering algorithms IEEE Transactions on Neural Networks 16 3 2005 645 678 (Pubitemid 40718010)
113. C. Nolker, and H. Ritter Visual recognition of continuous hand postures IEEE Transactions on Neural Networks 13 4 2002 983 994