# ADMM-MM Algorithm for General Tensor Decomposition

arXiv: https://arxiv.org/abs/2312.11763 · HTML: https://mlsanity.com/paper/2312.11763/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 28 references that are in the map.
- First posted on arXiv 19 Dec 2023.

## Builds on (most cited first, 5 of 5)

- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Generalized Canonical Polyadic Tensor Decomposition](https://mlsanity.com/paper/1808.07452/) (2018)
- [A Flexible and Efficient Algorithmic Framework for Constrained Matrix and Tensor Factorization](https://mlsanity.com/paper/1506.04209/) (2015)

## Abstract (arXiv)

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 (ℓ2-loss, ℓ1-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.