# PARAFAC2-based Coupled Matrix and Tensor Factorizations

arXiv: https://arxiv.org/abs/2210.13054 · HTML: https://mlsanity.com/paper/2210.13054/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 24 Oct 2022.

## Builds on (most cited first, 7 of 7)

- [A Flexible and Efficient Algorithmic Framework for Constrained Matrix and Tensor Factorization](https://mlsanity.com/paper/1506.04209/) (2015)
- [Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach](https://mlsanity.com/paper/1804.05307/) (2018)
- [An AO-ADMM approach to constraining PARAFAC2 on all modes](https://mlsanity.com/paper/2110.01278/) (2021)
- [Nonnegative PARAFAC2: a flexible coupling approach](https://mlsanity.com/paper/1802.05035/) (2018)
- [TASTE: Temporal and Static Tensor Factorization for Phenotyping Electronic Health Records](https://mlsanity.com/paper/1911.05843/) (2019)
- [Tracing Network Evolution Using the PARAFAC2 Model](https://mlsanity.com/paper/1911.02926/) (2019)
- [A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings](https://mlsanity.com/paper/2007.09605/) (2020)

## Built on by (most cited first, 3 of 3)

- [Every Response Counts: Quantifying Uncertainty of LLM-based Multi-Agent Systems through Tensor Decomposition](https://mlsanity.com/paper/2604.08708/) (2026)
- [PARAFAC2-based Coupled Matrix and Tensor Factorizations with Constraints](https://mlsanity.com/paper/2406.12338/) (2024)
- [Fast Learnings of Coupled Nonnegative Tensor Decomposition Using Optimal Gradient and Low-rank Approximation](https://mlsanity.com/paper/2302.05119/) (2023)

## Abstract (arXiv)

Coupled matrix and tensor factorizations (CMTF) have emerged as an effective data fusion tool to jointly analyze data sets in the form of matrices and higher-order tensors. The PARAFAC2 model has shown to be a promising alternative to the CANDECOMP/PARAFAC (CP) tensor model due to its flexibility and capability to handle irregular/ragged tensors. While fusion models based on a PARAFAC2 model coupled with matrix/tensor decompositions have been recently studied, they are limited in terms of possible regularizations and/or types of coupling between data sets. In this paper, we propose an algorithmic framework for fitting PARAFAC2-based CMTF models with the possibility of imposing various constraints on all modes and linear couplings, using Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). Through numerical experiments, we demonstrate that the proposed algorithmic approach accurately recovers the underlying patterns using various constraints and linear couplings.