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