Randomized Tensor Ring Decomposition and Its Application to Large-scale Data Reconstruction
Longhao Yuan, Chao Li, Jianting Cao, Qibin Zhao
TL;DR
This work tackles the high computational cost of tensor ring (TR) decomposition for large-scale data by introducing randomized TR decomposition (rTRD) based on tensor random projection (TRP). By projecting each mode with Gaussian (and orthogonal) projections to obtain a small tensor $\boldsymbol{\mathcal{P}}$, solving TR on $\boldsymbol{\mathcal{P}}$ via TRALS or TRSVD, and back-projecting to obtain the TR factors $\boldsymbol{\mathcal{G}}_n$, the authors derive two algorithms: rTRALS and rTRSVD. The approach delivers 4–25× speedups without sacrificing accuracy and shows superior performance in deep-learning data compression and hyperspectral image reconstruction compared with other randomized methods. This randomized TR framework enables scalable, high-quality tensor reconstructions for very large datasets and opens avenues for handling sparse or incomplete tensors in future work.
Abstract
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR decomposition algorithms suffer from high computational cost when facing large-scale data. In this paper, taking advantages of the recently proposed tensor random projection method, we propose two TR decomposition algorithms. By employing random projection on every mode of the large-scale tensor, the TR decomposition can be processed at a much smaller scale. The simulation experiment shows that the proposed algorithms are $4-25$ times faster than traditional algorithms without loss of accuracy, and our algorithms show superior performance in deep learning dataset compression and hyperspectral image reconstruction experiments compared to other randomized algorithms.