Weijun Sun

Yichun Qiu, Weijun Sun, Guoxu Zhou et al. · tsinghua

Efficient and accurate low-rank approximation (LRA) methods are of great significance for large-scale data analysis. Randomized tensor decompositions have emerged as powerful tools to meet this need, but most existing methods perform poorly in the presence of noise interference. Inspired by the remarkable performance of randomized block Krylov iteration (rBKI) in reducing the effect of tail singular values, this work designs an rBKI-based Tucker decomposition (rBKI-TK) for accurate approximation, together with a hierarchical tensor ring decomposition based on rBKI-TK for efficient compression of large-scale data. Besides, the error bound between the deterministic LRA and the randomized LRA is studied. Numerical experiences demonstrate the efficiency, accuracy and scalability of the proposed methods in both data compression and denoising.

Peilin Yang, Yonghui Huang, Yuning Qiu et al.

Tensor completion aimes at recovering missing data, and it is one of the popular concerns in deep learning and signal processing. Among the higher-order tensor decomposition algorithms, the recently proposed fully-connected tensor network decomposition (FCTN) algorithm is the most advanced. In this paper, by leveraging the superior expression of the fully-connected tensor network (FCTN) decomposition, we propose a new tensor completion method named the fully connected tensor network weighted optization(FCTN-WOPT). The algorithm performs a composition of the completed tensor by initialising the factors from the FCTN decomposition. We build a loss function with the weight tensor, the completed tensor and the incomplete tensor together, and then update the completed tensor using the lbfgs gradient descent algorithm to reduce the spatial memory occupation and speed up iterations. Finally we test the completion with synthetic data and real data (both image data and video data) and the results show the advanced performance of our FCTN-WOPT when it is applied to higher-order tensor completion.

Peilin Yang, Weijun Sun, Qibin Zhao et al.

The prevalent fully-connected tensor network (FCTN) has achieved excellent success to compress data. However, the FCTN decomposition suffers from slow computational speed when facing higher-order and large-scale data. Naturally, there arises an interesting question: can a new model be proposed that decomposes the tensor into smaller ones and speeds up the computation of the algorithm? This work gives a positive answer by formulating a novel higher-order tensor decomposition model that utilizes latent matrices based on the tensor network structure, which can decompose a tensor into smaller-scale data than the FCTN decomposition, hence we named it Latent Matrices for Tensor Network Decomposition (LMTN). Furthermore, three optimization algorithms, LMTN-PAM, LMTN-SVD and LMTN-AR, have been developed and applied to the tensor-completion task. In addition, we provide proofs of theoretical convergence and complexity analysis for these algorithms. Experimental results show that our algorithm has the effectiveness in both deep learning dataset compression and higher-order tensor completion, and that our LMTN-SVD algorithm is 3-6 times faster than the FCTN-PAM algorithm and only a 1.8 points accuracy drop.