# Tracing Network Evolution Using the PARAFAC2 Model

arXiv: https://arxiv.org/abs/1911.02926 · HTML: https://mlsanity.com/paper/1911.02926/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2019.

## 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)
- [PARAFAC2-based Coupled Matrix and Tensor Factorizations](https://mlsanity.com/paper/2210.13054/) (2022)
- [Advancing Security in AI Systems: A Novel Approach to Detecting Backdoors in Deep Neural Networks](https://mlsanity.com/paper/2403.08208/) (2024)
- [PARAFAC2 AO-ADMM: Constraints in all modes](https://mlsanity.com/paper/2102.02087/) (2021)
- [A Time-aware tensor decomposition for tracking evolving patterns](https://mlsanity.com/paper/2308.07126/) (2023)
- [FCNCP: A Coupled Nonnegative CANDECOMP/PARAFAC Decomposition Based on Federated Learning](https://mlsanity.com/paper/2404.11890/) (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)
- [Frequency-domain alignment of heterogeneous, multidimensional separations data through complex orthogonal Procrustes analysis](https://mlsanity.com/paper/2502.12810/) (2025)
- [dCMF: Learning interpretable evolving patterns from temporal multiway data](https://mlsanity.com/paper/2502.19367/) (2025)

## Abstract (arXiv)

Characterizing time-evolving networks is a challenging task, but it is crucial for understanding the dynamic behavior of complex systems such as the brain. For instance, how spatial networks of functional connectivity in the brain evolve during a task is not well-understood. A traditional approach in neuroimaging data analysis is to make simplifications through the assumption of static spatial networks. In this paper, without assuming static networks in time and/or space, we arrange the temporal data as a higher-order tensor and use a tensor factorization model called PARAFAC2 to capture underlying patterns (spatial networks) in time-evolving data and their evolution. Numerical experiments on simulated data demonstrate that PARAFAC2 can successfully reveal the underlying networks and their dynamics. We also show the promising performance of the model in terms of tracing the evolution of task-related functional connectivity in the brain through the analysis of functional magnetic resonance imaging data.