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Mathematical Problems in Engineering
Volume 2017, Article ID 3818949, 11 pages
https://doi.org/10.1155/2017/3818949
Research Article

Least Square Support Tensor Regression Machine Based on Submatrix of the Tensor

College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China

Correspondence should be addressed to Zhi-Xia Yang; moc.anis@xhzgnayjx

Received 14 March 2017; Revised 10 October 2017; Accepted 15 October 2017; Published 9 November 2017

Academic Editor: Gisella Tomasini

Copyright © 2017 Tuo Shu and Zhi-Xia Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For tensor regression problem, a novel method, called least square support tensor regression machine based on submatrix of a tensor (LS-STRM-SMT), is proposed. LS-STRM-SMT is a method which can be applied to deal with tensor regression problem more efficiently. First, we develop least square support matrix regression machine (LS-SMRM) and propose a fixed point algorithm to solve it. And then LS-STRM-SMT for tensor data is proposed. Inspired by the relation between photochrome and the gray pictures, we reformulate the tensor sample training set and form the new model (LS-STRM-SMT) for tensor regression problem. With the introduction of projection matrices and another fixed point algorithm, we turn the LS-STRM-SMT model into several related LS-SMRM models which are solved by the algorithm for LS-SMRM. Since the fixed point algorithm is used twice while solving the LS-STRM-SMT problem, we call the algorithm dual fixed point algorithm (DFPA). Our method (LS-STRM-SMT) has been compared with several typical support tensor regression machines (STRMs). From theoretical point of view, our algorithm has less parameters and its computational complexity should be lower, especially when the rank of submatrix is small. The numerical experiments indicate that our algorithm has a better performance.