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arXiv · 2308.01480

A Randomized Block Krylov Method for Tensor Train Approximation

Gaohang Yu·Jinhong Feng·Zhongming Chen·Xiaohao Cai·Liqun Qi
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Abstract

Tensor train decomposition is a powerful tool for dealing with high-dimensional, large-scale tensor data, which is not suffering from the curse of dimensionality. To accelerate the calculation of the auxiliary unfolding matrix, some randomized algorithms have been proposed; however, they are not suitable for noisy data. The randomized block Krylov method is capable of dealing with heavy-tailed noisy data in the low-rank approximation of matrices. In this paper, we present a randomized algorithm for low-rank tensor train approximation of large-scale tensors based on randomized block Krylov subspace iteration and provide theoretical guarantees. Numerical experiments on synthetic and real-world tensor data demonstrate the effectiveness of the proposed algorithm.

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Gaohang Yu, Jinhong Feng, Zhongming Chen, Xiaohao Cai, Liqun Qi. 2023-08-03. A Randomized Block Krylov Method for Tensor Train Approximation. https://arxiv.org/abs/2308.01480

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