# tPARAFAC2: Tracking evolving patterns in (incomplete) temporal data

arXiv: https://arxiv.org/abs/2407.01356 · HTML: https://mlsanity.com/paper/2407.01356/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Builds on (most cited first, 13 of 13)

- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [The Dynamic Embedded Topic Model](https://mlsanity.com/paper/1907.05545/) (2019)
- [A Flexible and Efficient Algorithmic Framework for Constrained Matrix and Tensor Factorization](https://mlsanity.com/paper/1506.04209/) (2015)
- [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)
- [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)
- [A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings](https://mlsanity.com/paper/2007.09605/) (2020)
- [Identifying and Alleviating Concept Drift in Streaming Tensor Decomposition](https://mlsanity.com/paper/1804.09619/) (2018)
- [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)
- [On Large-Scale Dynamic Topic Modeling with Nonnegative CP Tensor Decomposition](https://mlsanity.com/paper/2001.00631/) (2020)

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

- [dCMF: Learning interpretable evolving patterns from temporal multiway data](https://mlsanity.com/paper/2502.19367/) (2025)

## Abstract (arXiv)

Tensor factorizations have been widely used for the task of uncovering patterns in various domains. Often, the input is time-evolving, shifting the goal to tracking the evolution of the underlying patterns instead. To adapt to this more complex setting, existing methods incorporate temporal regularization but they either have overly constrained structural requirements or lack uniqueness which is crucial for interpretation. In this paper, in order to capture the underlying evolving patterns, we introduce t(emporal)PARAFAC2, which utilizes temporal smoothness regularization on the evolving factors. Previously, Alternating Optimization (AO) and Alternating Direction Method of Multipliers (ADMM)-based algorithmic approach has been introduced to fit the PARAFAC2 model to fully observed data. In this paper, we extend this algorithmic framework to the case of partially observed data and use it to fit the tPARAFAC2 model to complete and incomplete datasets with the goal of revealing evolving patterns. Our numerical experiments on simulated datasets demonstrate that tPARAFAC2 can extract the underlying evolving patterns more accurately compared to the state-of-the-art in the presence of high amounts of noise and missing data. Using two real datasets, we also demonstrate the effectiveness of the algorithmic approach in terms of handling missing data and tPARAFAC2 model in terms of revealing evolving patterns. The paper provides an extensive comparison of different approaches for handling missing data within the proposed framework, and discusses both the advantages and limitations of tPARAFAC2 model.