  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.
