Randomized Algorithms for Computing the Generalized Tensor SVD Based on the Tensor Product

This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tensor product (T-product). The random projection method is utilized to compute the important actions of the underlying data tensors and use them to get small sketches of the original data tensors, which are easier to handle. Due to the small size of the tensor sketches, deterministic approaches are applied to them to compute their GTSVD. Then, from the GTSVD of the small tensor sketches, the GTSVD of the original large-scale data tensors is recovered. Some experiments are conducted to show the effectiveness of the proposed approach. © Shanghai University 2024.