# Fast and Accurate Dual-Way Streaming PARAFAC2 for Irregular Tensors -- Algorithm and Application

arXiv: https://arxiv.org/abs/2305.18376 · HTML: https://mlsanity.com/paper/2305.18376/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 43 references that are in the map.
- First posted on arXiv 28 May 2023.

## Builds on (most cited first, 6 of 6)

- [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)
- [Identifying and Alleviating Concept Drift in Streaming Tensor Decomposition](https://mlsanity.com/paper/1804.09619/) (2018)
- [Robust Factorization of Real-world Tensor Streams with Patterns, Missing Values, and Outliers](https://mlsanity.com/paper/2102.08466/) (2021)
- [DPar2: Fast and Scalable PARAFAC2 Decomposition for Irregular Dense Tensors](https://mlsanity.com/paper/2203.12798/) (2022)
- [Inductive Framework for Multi-Aspect Streaming Tensor Completion with Side Information](https://mlsanity.com/paper/1802.06371/) (2018)

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

- [Fast Mining and Dynamic Time-to-Event Prediction over Multi-sensor Data Streams](https://mlsanity.com/paper/2601.04741/) (2026)

## Abstract (arXiv)

How can we efficiently and accurately analyze an irregular tensor in a dual-way streaming setting where the sizes of two dimensions of the tensor increase over time? What types of anomalies are there in the dual-way streaming setting? An irregular tensor is a collection of matrices whose column lengths are the same while their row lengths are different. In a dual-way streaming setting, both new rows of existing matrices and new matrices arrive over time. PARAFAC2 decomposition is a crucial tool for analyzing irregular tensors. Although real-time analysis is necessary in the dual-way streaming, static PARAFAC2 decomposition methods fail to efficiently work in this setting since they perform PARAFAC2 decomposition for accumulated tensors whenever new data arrive. Existing streaming PARAFAC2 decomposition methods work in a limited setting and fail to handle new rows of matrices efficiently. In this paper, we propose Dash, an efficient and accurate PARAFAC2 decomposition method working in the dual-way streaming setting. When new data are given, Dash efficiently performs PARAFAC2 decomposition by carefully dividing the terms related to old and new data and avoiding naive computations involved with old data. Furthermore, applying a forgetting factor makes Dash follow recent movements. Extensive experiments show that Dash achieves up to 14.0x faster speed than existing PARAFAC2 decomposition methods for newly arrived data. We also provide discoveries for detecting anomalies in real-world datasets, including Subprime Mortgage Crisis and COVID-19.