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arXiv · 2309.02877

A multilinear Nystr\"om algorithm for low-rank approximation of tensors in Tucker format

Alberto Bucci·Leonardo Robol
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Abstract

The Nystr\"om 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 Nystr\"om 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 Nystr\"om's methodology tailored to approximating low-rank tensors in the Tucker format: the multilinear Nystr\"om 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 Nystr\"om method, positioning it as a viable substitute for the randomized higher-order SVD algorithm.

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Alberto Bucci, Leonardo Robol. 2023-09-06. A multilinear Nystr\"om algorithm for low-rank approximation of tensors in Tucker format. https://arxiv.org/abs/2309.02877

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