Latent Matrices for Tensor Network Decomposition and to Tensor Completion
This work addresses computational bottlenecks in tensor decomposition for researchers and practitioners in data compression and tensor completion, though it appears incremental as it builds upon existing FCTN methods.
The authors tackled the slow computational speed of fully-connected tensor network (FCTN) decomposition for higher-order and large-scale data by proposing a novel model called Latent Matrices for Tensor Network Decomposition (LMTN), which decomposes tensors into smaller-scale data and speeds up computation, with their LMTN-SVD algorithm showing 3-6 times faster performance than FCTN-PAM with only a 1.8 points accuracy drop.
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.