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.

翻译：张量的低秩逼近已广泛应用于高维数据分析，通常涉及大规模矩阵的奇异值分解（SVD），计算复杂度较高。草图技术是一种有效的数据压缩与降维方法，适用于大规模矩阵的低秩逼近。本文基于草图与幂方法，提出了两种实用的随机算法用于大规模张量的低秩Tucker逼近，并给出了严格的误差界分析。在合成张量数据和真实张量数据上的数值实验表明，所提算法具有竞争性性能。