# A Time-aware tensor decomposition for tracking evolving patterns

arXiv: https://arxiv.org/abs/2308.07126 · HTML: https://mlsanity.com/paper/2308.07126/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 14 Aug 2023.

## Builds on (most cited first, 8 of 8)

- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [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)
- [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)

## Built on by (most cited first, 2 of 2)

- [tPARAFAC2: Tracking evolving patterns in (incomplete) temporal data](https://mlsanity.com/paper/2407.01356/) (2024)
- [dCMF: Learning interpretable evolving patterns from temporal multiway data](https://mlsanity.com/paper/2502.19367/) (2025)

## Abstract (arXiv)

Time-evolving data sets can often be arranged as a higher-order tensor with one of the modes being the time mode. While tensor factorizations have been successfully used to capture the underlying patterns in such higher-order data sets, the temporal aspect is often ignored, allowing for the reordering of time points. In recent studies, temporal regularizers are incorporated in the time mode to tackle this issue. Nevertheless, existing approaches still do not allow underlying patterns to change in time (e.g., spatial changes in the brain, contextual changes in topics). In this paper, we propose temporal PARAFAC2 (tPARAFAC2): a PARAFAC2-based tensor factorization method with temporal regularization to extract gradually evolving patterns from temporal data. Through extensive experiments on synthetic data, we demonstrate that tPARAFAC2 can capture the underlying evolving patterns accurately performing better than PARAFAC2 and coupled matrix factorization with temporal smoothness regularization.