Least Square Support Tensor Regression Machine Based on Submatrix of the Tensor
Least Square Support Tensor Regression Machine Based on Submatrix of the Tensor
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DOI：
10.1155/2017/3818949
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发表时间：
2017-11
影响因子：
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通讯作者：
Tuo Shu;Zhixia Yang
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文献类型：
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作者：
Tuo Shu;Zhixia Yang
针对张量回归问题，提出了一种基于张量子矩阵的最小二乘支持张量回归机（LS-STRM-SMT）方法。LS-STRM-SMT是一种可以更有效地处理张量回归问题的方法。首先，我们开发了最小二乘支持矩阵回归机（LS-SMRM），并提出了求解它的不动点算法。然后提出了张量数据的LS-STRM-SMT方法。受photochrome与灰度图像之间关系的启发，我们重新构造了张量样本训练集，形成了张量回归问题的新模型LS-STRM-SMT。通过引入投影矩阵和另一种不动点算法，将LS-STRM-SMT模型转化为若干相关的LS-SMRM模型，并用LS-SMRM算法求解。由于在求解LS-STRM-SMT问题时使用了两次不动点算法，因此我们称该算法为对偶不动点算法（DFPA）。我们的方法（LS-STRM-SMT）与几种典型的支持张量回归机（strm）进行了比较。从理论上讲，我们的算法参数更少，计算复杂度更低，特别是当子矩阵的秩较小时。数值实验表明，该算法具有较好的性能。
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.