# DPar2: Fast and Scalable PARAFAC2 Decomposition for Irregular Dense Tensors

arXiv: https://arxiv.org/abs/2203.12798 · HTML: https://mlsanity.com/paper/2203.12798/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 24 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [FMA: A Dataset For Music Analysis](https://mlsanity.com/paper/1612.01840/) (2016)
- [Multivariate LSTM-FCNs for Time Series Classification](https://mlsanity.com/paper/1801.04503/) (2018)
- [Fast and Guaranteed Tensor Decomposition via Sketching](https://mlsanity.com/paper/1506.04448/) (2015)
- [COPA: Constrained PARAFAC2 for Sparse & Large Datasets](https://mlsanity.com/paper/1803.04572/) (2018)
- [SPARTan: Scalable PARAFAC2 for Large & Sparse Data](https://mlsanity.com/paper/1703.04219/) (2017)
- [TASTE: Temporal and Static Tensor Factorization for Phenotyping Electronic Health Records](https://mlsanity.com/paper/1911.05843/) (2019)
- [SliceNStitch: Continuous CP Decomposition of Sparse Tensor Streams](https://mlsanity.com/paper/2102.11517/) (2021)
- [Parallel Tensor Compression for Large-Scale Scientific Data](https://mlsanity.com/paper/1510.06689/) (2015)
- [Supervised and Extended Restart in Random Walks for Ranking and Link Prediction in Networks](https://mlsanity.com/paper/1710.06609/) (2017)

## Built on by (most cited first, 4 of 4)

- [D-Tracker: Modeling Interest Diffusion in Social Activity Tensor Data Streams](https://mlsanity.com/paper/2505.00242/) (2025)
- [Fast and Accurate Dual-Way Streaming PARAFAC2 for Irregular Tensors -- Algorithm and Application](https://mlsanity.com/paper/2305.18376/) (2023)
- [SWoTTeD: An Extension of Tensor Decomposition to Temporal Phenotyping](https://mlsanity.com/paper/2310.01201/) (2023)
- [Interpretable Dynamic Network Modeling of Tensor Time Series via Kronecker Time-Varying Graphical Lasso](https://mlsanity.com/paper/2602.08197/) (2026)

## Abstract (arXiv)

Given an irregular dense tensor, how can we efficiently analyze it? An irregular tensor is a collection of matrices whose columns have the same size and rows have different sizes from each other. PARAFAC2 decomposition is a fundamental tool to deal with an irregular tensor in applications including phenotype discovery and trend analysis. Although several PARAFAC2 decomposition methods exist, their efficiency is limited for irregular dense tensors due to the expensive computations involved with the tensor. In this paper, we propose DPar2, a fast and scalable PARAFAC2 decomposition method for irregular dense tensors. DPar2 achieves high efficiency by effectively compressing each slice matrix of a given irregular tensor, careful reordering of computations with the compression results, and exploiting the irregularity of the tensor. Extensive experiments show that DPar2 is up to 6.0x faster than competitors on real-world irregular tensors while achieving comparable accuracy. In addition, DPar2 is scalable with respect to the tensor size and target rank.