ADMM-MM Algorithm for General Tensor Decomposition
This provides a flexible optimization framework for tensor decomposition problems across different applications, though it appears incremental as it combines existing methods.
The authors tackled the problem of general tensor decomposition in linear observation models by proposing a unified optimization algorithm that supports multiple loss functions and decomposition models. They achieved this through a hierarchical combination of ADMM and MM methods, enabling plug-and-play extension to various tensor decomposition models.
In this paper, we propose a new unified optimization algorithm for general tensor decomposition which is formulated as an inverse problem for low-rank tensors in the general linear observation models. The proposed algorithm supports three basic loss functions ($\ell_2$-loss, $\ell_1$-loss and KL divergence) and various low-rank tensor decomposition models (CP, Tucker, TT, and TR decompositions). We derive the optimization algorithm based on hierarchical combination of the alternating direction method of multiplier (ADMM) and majorization-minimization (MM). We show that wide-range applications can be solved by the proposed algorithm, and can be easily extended to any established tensor decomposition models in a {plug-and-play} manner.