Latent Matrices for Tensor Network Decomposition and to Tensor Completion

TL;DR

This paper introduces LMTN, a novel tensor decomposition model using latent matrices that decomposes tensors into smaller parts, significantly speeding up computation and improving efficiency in tensor completion tasks.

Contribution

The paper proposes a new higher-order tensor decomposition model, LMTN, with three optimization algorithms, and provides theoretical convergence proofs and complexity analysis.

Findings

LMTN-SVD is 3-6 times faster than FCTN-PAM.

LMTN maintains comparable accuracy with only 1.8 points drop.

Effective in deep learning dataset compression and tensor completion.

Abstract

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.