Efficient Tensor Robust PCA under Hybrid Model of Tucker and Tensor Train
This work addresses computational bottlenecks in tensor recovery for machine learning and computer vision applications, representing an incremental improvement over existing methods.
The paper tackled the high computational complexity of tensor robust principal component analysis (TRPCA) for large-scale tensor data by proposing an efficient hybrid model combining Tucker and tensor train decompositions, which reduced computational costs and demonstrated superiority in numerical experiments on synthetic and real-world data.
Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor recovery tasks. However, due to the large-scale tensor data in real-world applications, previous TRPCA models often suffer from high computational complexity. In this letter, we propose an efficient TRPCA under hybrid model of Tucker and TT. Specifically, in theory we reveal that TT nuclear norm (TTNN) of the original big tensor can be equivalently converted to that of a much smaller tensor via a Tucker compression format, thereby significantly reducing the computational cost of singular value decomposition (SVD). Numerical experiments on both synthetic and real-world tensor data verify the superiority of the proposed model.