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：在高维数据分析中,广泛使用低位粒子近似值,通常涉及计算复杂度高的大型基质的单值分解(SVD),密片是适用于大基质低位近似值的有效数据压缩和维度减少技术,本文介绍了基于草图和动力法的大型塔克低位压子近似值两种实用随机算法,并进行了严格的有误分析。合成和现实世界的抗量数据的数值实验显示了拟议算法的竞争性性能。