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Nov. 27, 2005 to Nov. 30, 2005
ISBN: 0-7695-2278-5
pp: 450-457
Dacheng Tao , University of London
Xuelong Li , University of London
Weiming Hu , Chinese Academy of Science
Stephen Maybank , University of London
Xindong Wu , University of Vermont
This paper aims to take general tensors as inputs for supervised learning. A supervised tensor learning (STL) framework is established for convex optimization based learning techniques such as support vector machines (SVM) and minimax probability machines (MPM). Within the STL framework, many conventional learning machines can be generalized to take n^th-order tensors as inputs. We also study the applications of tensors to learning machine design and feature extraction by linear discriminant analysis (LDA). Our method for tensor based feature extraction is named the tenor rank-one discriminant analysis (TR1DA). These generalized algorithms have several advantages: 1) reduce the curse of dimension problem in machine learning and data mining; 2) avoid the failure to converge; and 3) achieve better separation between the different categories of samples. As an example, we generalize MPM to its STL version, which is named the tensor MPM (TMPM). TMPM learns a series of tensor projections iteratively. It is then evaluated against the original MPM. Our experiments on a binary classification problem show that TMPM significantly outperforms the original MPM.
Dacheng Tao, Xuelong Li, Weiming Hu, Stephen Maybank, Xindong Wu, "Supervised Tensor Learning", ICDM, 2005, Proceedings. Fifth IEEE International Conference on Data Mining, Proceedings. Fifth IEEE International Conference on Data Mining 2005, pp. 450-457, doi:10.1109/ICDM.2005.139
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