This web site aims to provide an overview of resources concerned with theories and applications of multilinear subspace learning (MSL). The origin of MSL traces back to multiway analysis in the 1960s and they have been studied extensively in face and gait recognition. With more connections revealed and analogies drawn between multilinear algorithms and their linear counterparts, MSL has become an exciting area to explore for applications involving largescale multidimensional (tensorial) data as well as a challenging problem for machine learning researchers to tackle.
Book & SurveyMultilinear Subspace Learning: Dimensionality Reduction of Multidimensional Data, Haiping Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, Chapman & Hall/CRC Press Machine Learning and Pattern Recognition Series, Taylor and Francis, ISBN: 9781439857243, 2013. A Survey of Multilinear Subspace Learning for Tensor Data, Haiping Lu, K. N. Plataniotis, and A. Venetsanopoulos, Pattern Recognition, Vol. 44, No. 7, pp. 15401551, Jul. 2011. SoftwareOpen source software on multilinear subspace learning algorithms:
DataThe FERET face data [2D tensor (matrix)] and training/test
partitions: The CMU PIE face data [2D tensor (matrix)] and training/test partitions: PIEP3I3 (10.2M). The USF gait data version 1.7 [3D tensor]: 128x88x20 (21.2M); 64x44x20 (9.9M); 32x22x10 (3.2M). Related Web SitesWikipedia entry on Multilinear Subspace Learning. BibliographyPapers relevant to MSL are ordered below according to topic, with occasional papers occuring under multiple headings.
TutorialsTutorial materials suitable for a first introduction to MSL. Prerequisites: elementary probability theory, statistics and linear algebra.H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, Multilinear Subspace Learning: Dimensionality Reduction of Multidimensional Data, Chapman & Hall/CRC Press Machine Learning and Pattern Recognition Series, Taylor and Francis, ISBN: 9781439857243, 2013. H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, A Survey of Multilinear Subspace Learning for Tensor Data, Pattern Recognition, Vol. 44, No. 7, pp. 15401551, Jul. 2011. T. G. Kolda, B. W. Bader, Tensor decompositions and applications, SIAM Review, Vol. 51, No. 3, pp. 455500, 2009. L. D. Lathauwer, B. D. Moor, J. Vandewalle, On the best rank1 and rank(R1, R2, ..., RN ) approximation of higherorder tensors, SIAM Journal of Matrix Analysis and Applications 21 (4) (2000) 13241342. L.D. Lathauwer, B.D. Moor, J. Vandewalle, A multilinear singular value decomposition, SIAM Journal of Matrix Analysis and Applications vol. 21, no. 4, pp. 12531278, 2000. MSL through TensortoTensor ProjectionMSL algorithms that project a tensor directly to another tensor of lower dimension.H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, MPCA: Multilinear Principal Component Analysis of Tensor Objects, IEEE Trans. on Neural Networks, Vol. 19, No. 1, Page: 1839, Jan. 2008. D. Tao, X. Li, X. Wu, and S. J. Maybank, General tensor discriminant analysis and gabor features for gait recognition, IEEE Trans. Pattern Anal. Mach. Intell., vol. 29, no. 10, pp. 17001715, Oct. 2007. S. Yan, D. Xu, Q. Yang, L. Zhang, X. Tang, and H.J. Zhang, Discriminant analysis with tensor representation, in Proc. IEEE Conference on Computer Vision and Pattern Recognition, vol. I, June 2005, pp. 526532 X. He, D. Cai, P. Niyogi, Tensor subspace analysis, in: Advances in Neural Information Processing Systemsc 18 (NIPS), 2005 MSL through TensortoVector ProjectionMSL algorithms that project a tensor directly to a vector of lower dimension.H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, Uncorrelated Multilinear Principal Component Analysis for Unsupervised Multilinear Subspace Learning, IEEE Trans. on Neural Networks, Vol. 20, No. 11, Page: 18201836, Nov. 2009. H. Lu, K. N. Plataniotis, and A. N. Venetsanopoulos, Uncorrelated Multilinear Discriminant Analysis with Regularization and Aggregation for Tensor Object Recognition, IEEE Trans. on Neural Networks, Vol. 20, No. 1, Page: 103123, Jan. 2009.
