# Nonnegative PARAFAC2: a flexible coupling approach

arXiv: https://arxiv.org/abs/1802.05035 · HTML: https://mlsanity.com/paper/1802.05035/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2018.

## Built on by (most cited first, 11 of 11)

- [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)
- [Randomized Algorithms for Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2402.08134/) (2024)
- [PARAFAC2 AO-ADMM: Constraints in all modes](https://mlsanity.com/paper/2102.02087/) (2021)
- [PARAFAC2×N: Coupled Decomposition of Multi-modal Data with Drift in N Modes](https://mlsanity.com/paper/2205.03501/) (2022)
- [Untargeted Region of Interest Selection for GC-MS Data using a Pseudo F-Ratio Moving Window (psiFRMV)](https://mlsanity.com/paper/2208.00313/) (2022)
- [SWoTTeD: An Extension of Tensor Decomposition to Temporal Phenotyping](https://mlsanity.com/paper/2310.01201/) (2023)
- [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)
- [Multi-Channel Automatic Music Transcription Using Tensor Algebra](https://mlsanity.com/paper/2107.11250/) (2021)

## Abstract (arXiv)

Modeling variability in tensor decomposition methods is one of the challenges of source separation. One possible solution to account for variations from one data set to another, jointly analysed, is to resort to the PARAFAC2 model. However, so far imposing constraints on the mode with variability has not been possible. In the following manuscript, a relaxation of the PARAFAC2 model is introduced, that allows for imposing nonnegativity constraints on the varying mode. An algorithm to compute the proposed flexible PARAFAC2 model is derived, and its performance is studied on both synthetic and chemometrics data.