# PARAFAC2-based Coupled Matrix and Tensor Factorizations with Constraints

arXiv: https://arxiv.org/abs/2406.12338 · HTML: https://mlsanity.com/paper/2406.12338/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 63 references that are in the map.
- First posted on arXiv 18 Jun 2024.

## Builds on (most cited first, 11 of 11)

- [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)
- [COPA: Constrained PARAFAC2 for Sparse & Large Datasets](https://mlsanity.com/paper/1803.04572/) (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)
- [Using link and content over time for embedding generation in Dynamic Attributed Networks](https://mlsanity.com/paper/1807.06560/) (2018)
- [PARAFAC2-based Coupled Matrix and Tensor Factorizations](https://mlsanity.com/paper/2210.13054/) (2022)
- [PARAFAC2×N: Coupled Decomposition of Multi-modal Data with Drift in N Modes](https://mlsanity.com/paper/2205.03501/) (2022)

## Built on by (most cited first, 1 of 1)

- [Knowledge-guided Pattern Discovery via Coupled Tensor Factorizations](https://mlsanity.com/paper/2608.13234/) (2026)

## Abstract (arXiv)

Data fusion models based on Coupled Matrix and Tensor Factorizations (CMTF) have been effective tools for joint analysis of data from multiple sources. While the vast majority of CMTF models are based on the strictly multilinear CANDECOMP/PARAFAC (CP) tensor model, recently also the more flexible PARAFAC2 model has been integrated into CMTF models. PARAFAC2 tensor models can handle irregular/ragged tensors and have shown to be especially useful for modelling dynamic data with unaligned or irregular time profiles. However, existing PARAFAC2-based CMTF models have limitations in terms of possible regularizations on the factors and/or types of coupling between datasets. To address these limitations, in this paper we introduce a flexible algorithmic framework that fits PARAFAC2-based CMTF models using Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). The proposed framework allows to impose various constraints on all modes and linear couplings to other matrix-, CP- or PARAFAC2-models. Experiments on various simulated and a real dataset demonstrate the utility and versatility of the proposed framework as well as its benefits in terms of accuracy and efficiency in comparison with state-of-the-art methods.