基于张量核函数的支持张量机分类方法

Support Tensor Machine for Classification Based on Tensor-Kernel

以秩一支持张量机(Rank-one Support Tensor Machine,R1-STM)为代表的张量学习现已成为模式识别领域的一个研究热点,具有非常广泛的应用.秩一支持张量机是非凸优化问题,不但求解非常耗时,而且得到的解是局部最优解.基于张量核函数的支持张量机(Support Tensor Machine based on Tensor-Kernel,TK-STM)能够解决非线性分类问题,不仅继承了支持向量机(Support Vector Machine,SVM)的优点,而且保持了更多的张量结构信息,能够通过一步迭代得到全局最优解.数值试验部分采用了五个向量型数据集和七个张量型数据集,并且将TK-STM与SVM和R1-STM这两个经典算法在分类精度和训练时间上进行了比较,实验结果表明无论在分类效果上还是训练时间上,TK-STM都具有明显的优势,特别是在处理高维小样本数据集上.

Represented by Rank-one Support Tensor Machine(R1-STM),Tensor learning has become a hotspot in the field of pattern recognition,and it has been widely used.R1-STM is a non-convex optimization problem,it is very time-consuming and suffers from local optimal.Support Tensor Machine based on Tensor-Kernel(TK-STM)can solve nonlinear classification problem,and it not only inherits the merits of Support Vector Machine(SVM),but also keeps more structure information,and can get the global optimal solution through one-step iteration.In the numerical experiment,five vector-type datasets and seven tensortype datasets were used.Based on two aspects of classification accuracy and training time,we compared TK-STM with the classical methods of SVM and R1-STM,the results show that TK-STM has obvious advantages in both classify effect and training time,especially in the high dimensional and small sample size datasets.