# Robust Factorization of Real-world Tensor Streams with Patterns, Missing Values, and Outliers

arXiv: https://arxiv.org/abs/2102.08466 · HTML: https://mlsanity.com/paper/2102.08466/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 45 references that are in the map.
- First posted on arXiv 16 Feb 2021.

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

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Tensor Completion Algorithms in Big Data Analytics](https://mlsanity.com/paper/1711.10105/) (2017)
- [Robust Low-rank Tensor Recovery: Models and Algorithms](https://mlsanity.com/paper/1311.6182/) (2013)
- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Bayesian Robust Tensor Factorization for Incomplete Multiway Data](https://mlsanity.com/paper/1410.2386/) (2014)
- [Subspace Learning and Imputation for Streaming Big Data Matrices and Tensors](https://mlsanity.com/paper/1404.4667/) (2014)
- [Variational Bayesian Inference for Robust Streaming Tensor Factorization and Completion](https://mlsanity.com/paper/1809.02153/) (2018)
- [Discovering and Characterizing Mobility Patterns in Urban Spaces: A Study of Manhattan Taxi Data](https://mlsanity.com/paper/1601.05274/) (2016)

## Built on by (most cited first, 6 of 6)

- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [SliceNStitch: Continuous CP Decomposition of Sparse Tensor Streams](https://mlsanity.com/paper/2102.11517/) (2021)
- [Streaming data preprocessing via online tensor recovery for large environmental sensor networks](https://mlsanity.com/paper/2109.00596/) (2021)
- [Fast and Accurate Dual-Way Streaming PARAFAC2 for Irregular Tensors -- Algorithm and Application](https://mlsanity.com/paper/2305.18376/) (2023)
- [Multi-Dictionary Tensor Decomposition](https://mlsanity.com/paper/2309.09717/) (2023)
- [Disentangled Mode-Specific Representations for Tensor Time Series via Contrastive Learning](https://mlsanity.com/paper/2602.23663/) (2026)

## Abstract (arXiv)

Consider multiple seasonal time series being collected in real-time, in the form of a tensor stream. Real-world tensor streams often include missing entries (e.g., due to network disconnection) and at the same time unexpected outliers (e.g., due to system errors). Given such a real-world tensor stream, how can we estimate missing entries and predict future evolution accurately in real-time? In this work, we answer this question by introducing SOFIA, a robust factorization method for real-world tensor streams. In a nutshell, SOFIA smoothly and tightly integrates tensor factorization, outlier removal, and temporal-pattern detection, which naturally reinforce each other. Moreover, SOFIA integrates them in linear time, in an online manner, despite the presence of missing entries. We experimentally show that SOFIA is (a) robust and accurate: yielding up to 76% lower imputation error and 71% lower forecasting error; (b) fast: up to 935X faster than the second-most accurate competitor; and (c) scalable: scaling linearly with the number of new entries per time step.