Towards Efficient and Accurate Approximation: Tensor Decomposition Based on Randomized Block Krylov Iteration
This work addresses the need for efficient and accurate tensor decomposition methods in large-scale data analysis, particularly in noisy environments, representing an incremental improvement over existing randomized techniques.
The paper tackled the problem of low-rank approximation for large-scale data by developing a randomized block Krylov iteration-based Tucker decomposition (rBKI-TK) and a hierarchical tensor ring decomposition, resulting in improved efficiency, accuracy, and scalability in data compression and denoising.
Efficient and accurate low-rank approximation (LRA) methods are of great significance for large-scale data analysis. Randomized tensor decompositions have emerged as powerful tools to meet this need, but most existing methods perform poorly in the presence of noise interference. Inspired by the remarkable performance of randomized block Krylov iteration (rBKI) in reducing the effect of tail singular values, this work designs an rBKI-based Tucker decomposition (rBKI-TK) for accurate approximation, together with a hierarchical tensor ring decomposition based on rBKI-TK for efficient compression of large-scale data. Besides, the error bound between the deterministic LRA and the randomized LRA is studied. Numerical experiences demonstrate the efficiency, accuracy and scalability of the proposed methods in both data compression and denoising.