Randomized Tensor Ring Decomposition and Its Application to Large-scale Data Reconstruction
This work addresses efficiency issues in tensor decomposition for researchers and practitioners handling large-scale multi-way data, representing an incremental improvement over existing methods.
The paper tackled the high computational cost of tensor ring decomposition for large-scale data by proposing two algorithms using tensor random projection, achieving 4-25 times faster processing without accuracy loss and superior performance in dataset compression and image reconstruction.
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.