TR-STF: a fast and accurate tensor ring decomposition algorithm via defined scaled tri-factorization

This paper proposes an algorithm based on defined scaled tri-factorization (STF) for fast and accurate tensor ring (TR) decomposition. First, based on the fast tri-factorization approach, we define STF and design a corresponding algorithm that can more accurately represent various matrices while maintaining a similar level of computational time. Second, we apply sequential STFs to TR decomposition with theoretical proof and propose a stable (i.e., non-iterative) algorithm named TR-STF. It is a computationally more efficient algorithm than existing TR decomposition algorithms, which is beneficial when dealing with big data. Experiments on multiple randomly simulated data, highly oscillatory functions, and real-world data sets verify the effectiveness and high efficiency of the proposed TR-STF. For example, on the Pavia University data set, TR-STF is nearly 9240 and 39 times faster, respectively, and more accurate than algorithms based on alternating least squares and singular value decomposition. As an extension, we apply sequential STFs to tensor train (TT) decomposition and propose a non-iterative algorithm named TT-STF. Experimental results demonstrate the superiority of the proposed TT-STF compared with the state-of-the-art TT decomposition algorithm.

Automated summary

This paper proposes an algorithm based on defined scaled tri-factorization (STF) for fast and accurate tensor ring (TR) decomposition. The algorithm accurately represents various matrices while maintaining computational efficiency. Experimental results show that the proposed method is faster and more accurate than existing algorithms for TR decomposition and tensor train (TT) decomposition.