Towards efficient and accurate approximation: tensor decomposition based on randomized block Krylov iteration

Tensor decomposition methods are inefficient when dealing with low-rank approximation of large-scale data. Randomized tensor decomposition has emerged to meet this need, but most existing methods exhibit high computational costs in handling large-scale tensors and poor approximation accuracy in noisy data scenarios. In this work, a Tucker decomposition method based on randomized block Krylov iteration (rBKI-TK) is proposed to reduce computational complexity and guarantee approximation accuracy by employing cumulative sketches rather than randomized initialization to construct a better projection space with fewer iterations. In addition, a hierarchical tensor ring decomposition based on rBKI-TK is proposed to enhance the scalability of the rBKI-TK method. Numerical results demonstrate the efficiency and accuracy of the proposed methods in large-scale and noisy data processing.