Practical Sketching Algorithms for Low-Rank Tucker Approximation of Large Tensors

Wandi Dong; Gaohang Yu; Liqun Qi; Xiaohao Cai

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arXiv · 2301.11598

Practical Sketching Algorithms for Low-Rank Tucker Approximation of Large Tensors

Wandi Dong·Gaohang Yu·Liqun Qi·Xiaohao Cai

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Abstract

Low-rank approximation of tensors has been widely used in high-dimensional data analysis. It usually involves singular value decomposition (SVD) of large-scale matrices with high computational complexity. Sketching is an effective data compression and dimensionality reduction technique applied to the low-rank approximation of large matrices. This paper presents two practical randomized algorithms for low-rank Tucker approximation of large tensors based on sketching and power scheme, with a rigorous error-bound analysis. Numerical experiments on synthetic and real-world tensor data demonstrate the competitive performance of the proposed algorithms.

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Wandi Dong, Gaohang Yu, Liqun Qi, Xiaohao Cai. 2023-01-27. Practical Sketching Algorithms for Low-Rank Tucker Approximation of Large Tensors. https://arxiv.org/abs/2301.11598

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