Randomized algorithms for fast computation of low rank tensor ring model

Randomized algorithms are efficient techniques for big data tensor analysis. In this tutorial paper, we review and extend a variety of randomized algorithms for decomposing large-scale data tensors in Tensor Ring (TR) format. We discuss both adaptive and nonadaptive randomized algorithms for this task. Our main focus is on the random projection technique as an efficient randomized framework and how it can be used to decompose large-scale data tensors in the TR format. Simulations are provided to support the presentation and efficiency, and performance of the presented algorithms are compared.