A Multilinear Nyström Algorithm for Low-Rank Approximation of Tensors in Tucker Format

The Nyström method offers an effective way to obtain low-rank approximation of SPD matrices and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nyström method). It is a randomized, single-pass, streamable, cost-effective, and accurate alternative to the randomized SVD, and it facilitates the computation of several matrix low-rank factorizations. In this paper, we take these advancements a step further by introducing a higher-order variant of Nyström's methodology tailored to approximating low-rank tensors in the Tucker format: the multilinear Nyström technique. We show that, by introducing appropriate small modifications in the formulation of the higher-order method, strong stability properties can be obtained. This algorithm retains the key attributes of the generalized Nyström method, positioning it as a viable substitute for the randomized higher-order SVD algorithm.