A Robust Low-Rank Tensor Decomposition and Quantization based Compression Method

Tensor data is widely used in fields such as smart grids, cloud systems, and deep learning. As the scale of this data increases, storage and transmission costs rise significantly. Many tensor data exhibit low-rank structures, offering the potential for data compression through low-rank decomposition techniques. Tucker decomposition, a typical low-rank decomposition technique, achieves data compression and interpretability by capturing complex data correlations and representing the original tensor with a compact core tensor and factor matrices. However, the compression ratio provided by Tucker decomposition is often insufficient, particularly for large-scale tensors. To tackle this issue, we propose a robust low-rank tensor compression method that leverages Tucker decomposition with quantization and coding. Initially, we establish a robust Tucker decomposition framework that decomposes the low-rank tensor into a core tensor and factor matrices using well-designed Tucker rank-setting rules. This framework effectively handles noise and missing values. Subsequently, we conduct an in-depth analysis of the numerical characteristics of the core tensor and factor matrices within the Tucker decomposition framework. Based on their distinct characteristics, we design tailored quantization and coding schemes to compress the core tensor and factor matrices, respectively, thereby significantly improving the compression ratio of Tucker decomposition while maintaining high accu-racy. Through extensive experiments on four publicly available datasets (which can form 3 or 4 order tensors), we demonstrate that our approach can achieve compression ratios
$4\times-10\times$
higher than the best competitor, with recovery errors improved by 8% - 42%.