# Randomized Tensor Ring Decomposition and Its Application to Large-scale Data Reconstruction

arXiv: https://arxiv.org/abs/1901.01652 · HTML: https://mlsanity.com/paper/1901.01652/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2019.

## Built on by (most cited first, 11 of 11)

- [More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees](https://mlsanity.com/paper/2110.07631/) (2021)
- [Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation](https://mlsanity.com/paper/2305.11495/) (2023)
- [Sampling-Based Decomposition Algorithms for Arbitrary Tensor Networks](https://mlsanity.com/paper/2210.03828/) (2022)
- [Defensive Tensorization](https://mlsanity.com/paper/2110.13859/) (2021)
- [A Coupled Random Projection Approach to Large-Scale Canonical Polyadic Decomposition](https://mlsanity.com/paper/2105.04084/) (2021)
- [Efficient Tensor Contraction via Fast Count Sketch](https://mlsanity.com/paper/2106.13062/) (2021)
- [Fast Hypergraph Regularized Nonnegative Tensor Ring Factorization Based on Low-Rank Approximation](https://mlsanity.com/paper/2109.02314/) (2021)
- [Towards Efficient and Accurate Approximation: Tensor Decomposition Based on Randomized Block Krylov Iteration](https://mlsanity.com/paper/2211.14828/) (2022)
- [Scalable and Robust Tensor Ring Decomposition for Large-scale Data](https://mlsanity.com/paper/2305.09044/) (2023)
- [NeuronSeek: On Stability and Expressivity of Task-driven Neurons](https://mlsanity.com/paper/2506.15715/) (2025)
- [Architectural Design and Performance Analysis of FPGA based AI Accelerators: A Comprehensive Review](https://mlsanity.com/paper/2603.08740/) (2026)

## Abstract (arXiv)

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.