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Title:Learning with Tensor Representation
Author(s):Cai, Deng; He, Xiaofei; Han, Jiawei
tensor representation
Abstract:Most of the existing learning algorithms take vectors as their input data. A function is then learned in such a vector space for classification, clustering, or dimensionality reduction. However, in some situations, there is reason to consider data as tensors. For example, an image can be considered as a second order tensor and a video can be considered as a third order tensor. In this paper, we propose two novel algorithms called {\bf Support Tensor Machines} (STM) and {\bf Tensor Least Square} (TLS). These two algorithms operate in the tesnor space. Specifically, we represent data as the second order tensors (or, matrices) in \mathcal{R}^{n_1} \otimes \mathcal{R}^{n_2}, where \mathcal{R}^{n_1} and \mathcal{R}^{n_2} are two vector spaces. STM aims at finding a maximum margin classifier in the tensor space, while TLS aims at finding a minimum residual sum-of-squares classifier. With tensor representation, the number of parameters estimated by STM (TLS) can be greatly reduced. Therefore, our algorithms are especially suitable for small sample cases. We compare our proposed algorithms with SVM and the ordinary Least Square method on six databases. Experimental results show the effectiveness of our algorithms.
Issue Date:2006-04
Genre:Technical Report
Other Identifier(s):UIUCDCS-R-2006-2716
Rights Information:You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).
Date Available in IDEALS:2009-04-21

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