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Supervised tensor learning
Dacheng Tao; Xuelong Li; Xindong Wu; Weiming Hu; Stephen J. Maybank
AbstractTensor representation is helpful to reduce the small sample size problem in discriminative subspace selection. As pointed by this paper, this is mainly because the structure information of objects in computer vision research is a reasonable constraint to reduce the number of unknown parameters used to represent a learning model. Therefore, we apply this information to the vector-based learning and generalize the vector-based learning to the tensor-based learning as the supervised tensor learning (STL) framework, which accepts tensors as input. To obtain the solution of STL, the alternating projection optimization procedure is developed. The STL framework is a combination of the convex optimization and the operations in multilinear algebra. The tensor representation helps reduce the overfitting problem in vector-based learning. Based on STL and its alternating projection optimization procedure, we generalize support vector machines, minimax probability machine, Fisher discriminant analysis, and distance metric learning, to support tensor machines, tensor minimax probability machine, tensor Fisher discriminant analysis, and the multiple distance metrics learning, respectively. We also study the iterative procedure for feature extraction within STL. To examine the effectiveness of STL, we implement the tensor minimax probability machine for image classification. By comparing with minimax probability machine, the tensor version reduces the overfitting problem.
KeywordConvex Optimization Supervised Learning Tensor Alternating Projection
WOS HeadingsScience & Technology ; Technology
Indexed BySCI
WOS Research AreaComputer Science
WOS SubjectComputer Science, Artificial Intelligence ; Computer Science, Information Systems
WOS IDWOS:000249657900001
Citation statistics
Cited Times:202[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.Univ London, Sch Comp Sci & Informat Syst, London, England
2.Univ Vermont, Dept Comp Sci, Burlington, VT USA
3.Chinese Acad Sci, Inst Automat, Natl Lab Pattern Regnit, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Dacheng Tao,Xuelong Li,Xindong Wu,et al. Supervised tensor learning[J]. KNOWLEDGE AND INFORMATION SYSTEMS,2007,13(1):1-42.
APA Dacheng Tao,Xuelong Li,Xindong Wu,Weiming Hu,&Stephen J. Maybank.(2007).Supervised tensor learning.KNOWLEDGE AND INFORMATION SYSTEMS,13(1),1-42.
MLA Dacheng Tao,et al."Supervised tensor learning".KNOWLEDGE AND INFORMATION SYSTEMS 13.1(2007):1-42.
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