Practical sketching-based randomized tensor ring decomposition

Based on sketching techniques, we propose two practical randomized algorithms for tensor ring (TR) decomposition. Specifically, on the basis of defining new tensor products and investigating their properties, the two algorithms are devised by applying the Kronecker sub-sampled randomized Fourier transform and TensorSketch to the alternating least squares subproblems derived from the minimization problem of TR decomposition. From the former, we find an algorithmic framework based on random projection for randomized TR decomposition. We compare our proposals with the existing methods using both synthetic and real data. Numerical results show that they have quite decent performance in accuracy and computing time.