Fast Adaptive Cross Tubal Tensor Approximation

This paper deals with proposing a new efficient adaptive algorithm for the computation of tensor SVD (t-SVD). The proposed algorithm can estimate the tubal-rank of a given third-order tensor and the corresponding low tubal-rank approximation given an approximation tolerance. The main advantage of the proposed algorithm is using only a part of lateral and a horizontal slices at each iteration in its computations. So, it is applicable for decomposing large-scale data tensors. Simulations on synthetics and real-world datasets are provided and in some cases, we achieve more than one order of magnitude acceleration compared with the classical truncated t-SVD. It is shown that the proposed approach can potentially be used in deep learning and internet of things applications.