  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.
