# dCMF: Learning interpretable evolving patterns from temporal multiway data

arXiv: https://arxiv.org/abs/2502.19367 · HTML: https://mlsanity.com/paper/2502.19367/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 24 references that are in the map.
- First posted on arXiv 26 Feb 2025.

## Builds on (most cited first, 10 of 10)

- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [A Flexible and Efficient Algorithmic Framework for Constrained Matrix and Tensor Factorization](https://mlsanity.com/paper/1506.04209/) (2015)
- [An AO-ADMM approach to constraining PARAFAC2 on all modes](https://mlsanity.com/paper/2110.01278/) (2021)
- [SSMF: Shifting Seasonal Matrix Factorization](https://mlsanity.com/paper/2110.12763/) (2021)
- [Tracing Network Evolution Using the PARAFAC2 Model](https://mlsanity.com/paper/1911.02926/) (2019)
- [Dynamical spectral unmixing of multitemporal hyperspectral images](https://mlsanity.com/paper/1510.04238/) (2015)
- [Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks](https://mlsanity.com/paper/2303.10566/) (2023)
- [Using link and content over time for embedding generation in Dynamic Attributed Networks](https://mlsanity.com/paper/1807.06560/) (2018)
- [A Time-aware tensor decomposition for tracking evolving patterns](https://mlsanity.com/paper/2308.07126/) (2023)
- [tPARAFAC2: Tracking evolving patterns in (incomplete) temporal data](https://mlsanity.com/paper/2407.01356/) (2024)

## Abstract (arXiv)

Multiway datasets are commonly analyzed using unsupervised matrix and tensor factorization methods to reveal underlying patterns. Frequently, such datasets include timestamps and could correspond to, for example, health-related measurements of subjects collected over time. The temporal dimension is inherently different from the other dimensions, requiring methods that account for its intrinsic properties. Linear Dynamical Systems (LDS) are specifically designed to capture sequential dependencies in the observed data. In this work, we bridge the gap between tensor factorizations and dynamical modeling by exploring the relationship between LDS, Coupled Matrix Factorizations (CMF) and the PARAFAC2 model. We propose a time-aware coupled factorization model called d(ynamical)CMF that constrains the temporal evolution of the latent factors to adhere to a specific LDS structure. Using synthetic datasets, we compare the performance of dCMF with PARAFAC2 and t(emporal)PARAFAC2 which incorporates temporal smoothness. Our results show that dCMF and PARAFAC2-based approaches perform similarly when capturing smoothly evolving patterns that adhere to the PARAFAC2 structure. However, dCMF outperforms alternatives when the patterns evolve smoothly but deviate from the PARAFAC2 structure. Furthermore, we demonstrate that the proposed dCMF method enables to capture more complex dynamics when additional prior information about the temporal evolution is incorporated.