In this paper, we propose a new adaptive cross algorithm for computing a low tubal rank approximation of third-order tensors, with less memory and demands lower computational complexity than the truncated tensor SVD (t-SVD). This makes it applicable for decomposing large-scale tensors. We conduct numerical experiments on synthetic and real-world datasets to confirm the efficiency and feasibility of the proposed algorithm. The simulation results show more than one order of magnitude acceleration in the computation of low tubal rank (t-SVD) for largescale tensors. An application to pedestrian attribute recognition is also presented.

翻译：本文提出一种新的自适应交叉算法，用于计算三阶张量的低管秩近似，该算法所需内存少于截断张量SVD（t-SVD），且计算复杂度更低，因此适用于大规模张量的分解。我们在合成数据集和真实数据集上进行了数值实验，以验证所提算法的有效性和可行性。仿真结果表明，在大规模张量的低管秩（t-SVD）计算中，该方法实现了超过一个数量级的加速。此外，本文还展示了该算法在行人属性识别任务中的应用。