  This work deals with developing two fast randomized algorithms for computing
the generalized tensor singular value decomposition (GTSVD) based on the tubal
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 be handled. Due to
the small size of the sketch tensors, deterministic approaches are applied to
them to compute their GTSVDs. Then, from the GTSVD of the small sketch tensors,
the GTSVD of the original large-scale data tensors is recovered. Some
experiments are conducted to show the effectiveness of the proposed approach.
