Faculty of Computer, Guangdong University of Technology, Guangzhou 510006, China.
IEEE Trans Image Process. 2013 Jul;22(7):2911-20. doi: 10.1109/TIP.2013.2253485. Epub 2013 Mar 20.
There has been growing interest in developing more effective learning machines for tensor classification. At present, most of the existing learning machines, such as support tensor machine (STM), involve nonconvex optimization problems and need to resort to iterative techniques. Obviously, it is very time-consuming and may suffer from local minima. In order to overcome these two shortcomings, in this paper, we present a novel linear support higher-order tensor machine (SHTM) which integrates the merits of linear C-support vector machine (C-SVM) and tensor rank-one decomposition. Theoretically, SHTM is an extension of the linear C-SVM to tensor patterns. When the input patterns are vectors, SHTM degenerates into the standard C-SVM. A set of experiments is conducted on nine second-order face recognition datasets and three third-order gait recognition datasets to illustrate the performance of the proposed SHTM. The statistic test shows that compared with STM and C-SVM with the RBF kernel, SHTM provides significant performance gain in terms of test accuracy and training speed, especially in the case of higher-order tensors.
人们对于开发更有效的张量分类学习机器越来越感兴趣。目前，大多数现有的学习机器，如支持张量机（STM），都涉及非凸优化问题，需要采用迭代技术。显然，这非常耗时，并且可能会受到局部最小值的影响。为了克服这两个缺点，在本文中，我们提出了一种新的线性支持高阶张量机（SHTM），它集成了线性 C-支持向量机（C-SVM）和张量秩一分解的优点。从理论上讲，SHTM 是线性 C-SVM 向张量模式的扩展。当输入模式为向量时，SHTM 退化为标准的 C-SVM。我们在九个二阶人脸识别数据集和三个三阶步态识别数据集上进行了一组实验，以说明所提出的 SHTM 的性能。统计测试表明，与 STM 和具有 RBF 核的 C-SVM 相比，SHTM 在测试精度和训练速度方面都有显著的性能提升，特别是在高阶张量的情况下。
