# SliceNStitch: Continuous CP Decomposition of Sparse Tensor Streams

arXiv: https://arxiv.org/abs/2102.11517 · HTML: https://mlsanity.com/paper/2102.11517/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 23 Feb 2021.

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

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Fast Matrix Factorization for Online Recommendation with Implicit Feedback](https://mlsanity.com/paper/1708.05024/) (2017)
- [Dynamic Matrix Factorization with Priors on Unknown Values](https://mlsanity.com/paper/1507.06452/) (2015)
- [Near Optimal Sketching of Low-Rank Tensor Regression](https://mlsanity.com/paper/1709.07093/) (2017)
- [Robust Factorization of Real-world Tensor Streams with Patterns, Missing Values, and Outliers](https://mlsanity.com/paper/2102.08466/) (2021)
- [SamBaTen: Sampling-based Batch Incremental Tensor Decomposition](https://mlsanity.com/paper/1709.00668/) (2017)
- [Anomaly Detection in Road Networks Using Sliding-Window Tensor Factorization](https://mlsanity.com/paper/1803.04534/) (2018)
- [Adaptive Granularity in Tensors: A Quest for Interpretable Structure](https://mlsanity.com/paper/1912.09009/) (2019)
- [NeCPD: An Online Tensor Decomposition with Optimal Stochastic Gradient Descent](https://mlsanity.com/paper/2003.08844/) (2020)

## Built on by (most cited first, 5 of 5)

- [DPar2: Fast and Scalable PARAFAC2 Decomposition for Irregular Dense Tensors](https://mlsanity.com/paper/2203.12798/) (2022)
- [D-Tracker: Modeling Interest Diffusion in Social Activity Tensor Data Streams](https://mlsanity.com/paper/2505.00242/) (2025)
- [Multi-Aspect Mining and Anomaly Detection for Heterogeneous Tensor Streams](https://mlsanity.com/paper/2602.04917/) (2026)
- [Global and Local Structure Learning for Sparse Tensor Completion](https://mlsanity.com/paper/2503.20929/) (2025)
- [Interpretable Dynamic Network Modeling of Tensor Time Series via Kronecker Time-Varying Graphical Lasso](https://mlsanity.com/paper/2602.08197/) (2026)

## Abstract (arXiv)

Consider traffic data (i.e., triplets in the form of source-destination-timestamp) that grow over time. Tensors (i.e., multi-dimensional arrays) with a time mode are widely used for modeling and analyzing such multi-aspect data streams. In such tensors, however, new entries are added only once per period, which is often an hour, a day, or even a year. This discreteness of tensors has limited their usage for real-time applications, where new data should be analyzed instantly as it arrives. How can we analyze time-evolving multi-aspect sparse data 'continuously' using tensors where time is'discrete'? We propose SLICENSTITCH for continuous CANDECOMP/PARAFAC (CP) decomposition, which has numerous time-critical applications, including anomaly detection, recommender systems, and stock market prediction. SLICENSTITCH changes the starting point of each period adaptively, based on the current time, and updates factor matrices (i.e., outputs of CP decomposition) instantly as new data arrives. We show, theoretically and experimentally, that SLICENSTITCH is (1) 'Any time': updating factor matrices immediately without having to wait until the current time period ends, (2) Fast: with constant-time updates up to 464x faster than online methods, and (3) Accurate: with fitness comparable (specifically, 72 ~ 100%) to offline methods.