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 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 large-scale 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。与截断张量SVD（t-SVD）相比，该算法所需内存更少、计算复杂度更低，因而适用于大规模张量的分解。我们通过合成数据集与真实世界数据集的数值实验，验证了该算法的有效性与可行性。仿真结果表明，在大规模张量的低管秩（t-SVD）计算中，加速效果超过一个数量级。此外，还展示了该算法在行人属性识别中的应用。