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

## TL;DR

This paper introduces two randomized tensor ring decomposition algorithms that significantly reduce computational costs for large-scale data, achieving 4-25 times faster processing without accuracy loss and improving performance in data compression and image reconstruction.

## Contribution

The paper proposes novel randomized TR decomposition algorithms leveraging tensor random projection to efficiently handle large-scale data.

## Key findings

- Algorithms are 4-25 times faster than traditional methods.
- Maintains accuracy while reducing computational cost.
- Outperforms other randomized algorithms in experiments.

## 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.