Abstract: Based on the stochastic gradient descent method, this paper proposes online support tensor machine (OSTM) algorithm for tensor classification. In OSTM, its input patterns are tensors which are collected one by one in a sequence. In order to maintain the natural structure and correlation in the original tensor data, and reduce training time and memory space, OSTM algorithm applies tensor rank-one decomposition to replace the original tensor and assist tensor inner computation. The experiments on thirteen tensor datasets show that compared with the online support vector machine, OSTM can provide a significant improvement in training speed with comparable test accuracy, especially for higher-order tensors.

Key words: online learning, support tensor machine, support vector machine, tensor rank-one decomposition

摘要： 基于随机梯度下降法，提出了在线支持张量机（online support tensor machine，OSTM）算法。该算法的学习数据是张量模式，并以序列方式获取。算法利用张量秩一分解来代替原始张量辅助内积运算，不仅保持了原始张量的自然结构信息和关系，也极大地节省了存储空间和计算时间。在13个张量数据集上的实验表明，与在线支持向量机相比，在拥有可比的测试精度的情况下，在线支持张量机具有更快的训练速度，尤其对于高阶张量，其优越性更明显。

关键词: 在线学习, 支持张量机, 支持向量机, 张量秩一分解