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

TL;DR

This paper introduces two practical randomized sketching algorithms for low-rank Tucker approximation of large tensors, significantly reducing computational complexity while maintaining accuracy, validated through experiments on synthetic and real data.

Contribution

The paper proposes novel randomized algorithms utilizing sketching and power schemes for efficient low-rank tensor approximation with rigorous error analysis.

Findings

Algorithms achieve competitive accuracy

Significant reduction in computational complexity

Effective on synthetic and real-world data

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.