# A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings

arXiv: https://arxiv.org/abs/2007.09605 · HTML: https://mlsanity.com/paper/2007.09605/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2020.

## Built on by (most cited first, 10 of 10)

- [An AO-ADMM approach to constraining PARAFAC2 on all modes](https://mlsanity.com/paper/2110.01278/) (2021)
- [Unsupervised EHR-based Phenotyping via Matrix and Tensor Decompositions](https://mlsanity.com/paper/2209.00322/) (2022)
- [PARAFAC2-based Coupled Matrix and Tensor Factorizations](https://mlsanity.com/paper/2210.13054/) (2022)
- [Personalized Coupled Tensor Decomposition for Multimodal Data Fusion: Uniqueness and Algorithms](https://mlsanity.com/paper/2412.01102/) (2024)
- [PARAFAC2-based Coupled Matrix and Tensor Factorizations with Constraints](https://mlsanity.com/paper/2406.12338/) (2024)
- [tPARAFAC2: Tracking evolving patterns in (incomplete) temporal data](https://mlsanity.com/paper/2407.01356/) (2024)
- [Toward Temporal Causal Representation Learning with Tensor Decomposition](https://mlsanity.com/paper/2507.14126/) (2025)
- [Dictionary-based Low-Rank Approximations and the Mixed Sparse Coding problem](https://mlsanity.com/paper/2111.12399/) (2021)
- [Fast Learnings of Coupled Nonnegative Tensor Decomposition Using Optimal Gradient and Low-rank Approximation](https://mlsanity.com/paper/2302.05119/) (2023)
- [Knowledge-guided Pattern Discovery via Coupled Tensor Factorizations](https://mlsanity.com/paper/2608.13234/) (2026)

## Abstract (arXiv)

Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges in data fusion and require to employ various regularizations, constraints, loss functions and different types of coupling structures between datasets. In this paper, we propose a flexible algorithmic framework for coupled matrix and tensor factorizations which utilizes Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). The framework facilitates the use of a variety of constraints, loss functions and couplings with linear transformations in a seamless way. Numerical experiments on simulated and real datasets demonstrate that the proposed approach is accurate, and computationally efficient with comparable or better performance than available CMTF methods for Frobenius norm loss, while being more flexible. Using Kullback-Leibler divergence on count data, we demonstrate that the algorithm yields accurate results also for other loss functions.