Low-Rank Matrix and Tensor Decomposition Using Randomized Two-Sided Subspace Iteration With Application to Video Reconstruction

The low-rank approximation of big data matrices and tensors plays a pivotal role in many modern applications. Recently, the randomized subspace iteration has shown to be a powerful tool in approximating large matrices. In this paper we present a rank-revealing, two-sided variant of the randomized subspace iteration. Novelty of our work lies in the utilization of the unpivoted QR factorization, rather than the singular value decomposition (SVD), for factorizing the compressed matrix. We provide bounds on the rank-revealingness of our algorithm as well as bounds on the error of the low-rank approximations, in both 2- and Frobenius norm. In addition, we employ the proposed algorithm to efficiently compute the low rank tensor decomposition using the truncated higher-order SVD. We conduct tests on (i) two classes of matrices, and (ii) synthetic data tensor and real dataset to demonstrate the efficacy of the proposed algorithms.