# Low-Rank Tucker Approximation of a Tensor From Streaming Data

arXiv: https://arxiv.org/abs/1904.10951 · HTML: https://mlsanity.com/paper/1904.10951/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2019.

## Built on by (most cited first, 15 of 15)

- [Learning Mean-Field Equations from Particle Data Using WSINDy](https://mlsanity.com/paper/2110.07756/) (2021)
- [Generative modeling via tensor train sketching](https://mlsanity.com/paper/2202.11788/) (2022)
- [Fast and Accurate Randomized Algorithms for Low-rank Tensor Decompositions](https://mlsanity.com/paper/2104.01101/) (2021)
- [Approximately Optimal Core Shapes for Tensor Decompositions](https://mlsanity.com/paper/2302.03886/) (2023)
- [TenIPS: Inverse Propensity Sampling for Tensor Completion](https://mlsanity.com/paper/2101.00323/) (2021)
- [More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees](https://mlsanity.com/paper/2110.07631/) (2021)
- [Subquadratic Kronecker Regression with Applications to Tensor Decomposition](https://mlsanity.com/paper/2209.04876/) (2022)
- [Near-Linear Time and Fixed-Parameter Tractable Algorithms for Tensor Decompositions](https://mlsanity.com/paper/2207.07417/) (2022)
- [Randomized Algorithms for Scientific Computing (RASC)](https://mlsanity.com/paper/2104.11079/) (2021)
- [Effective Streaming Low-tubal-rank Tensor Approximation via Frequent Directions](https://mlsanity.com/paper/2108.10129/) (2021)
- [Efficient Tensor Contraction via Fast Count Sketch](https://mlsanity.com/paper/2106.13062/) (2021)
- [Sample Efficient Learning of Factored Embeddings of Tensor Fields](https://mlsanity.com/paper/2209.00372/) (2022)
- [Accelerating Large-Scale Regularized High-Order Tensor Recovery](https://mlsanity.com/paper/2506.09594/) (2025)
- [ACT-Tensor: Tensor Completion Framework for Financial Dataset Imputation](https://mlsanity.com/paper/2508.01861/) (2025)
- [Fast and Accurate SVD-Type Updating in Streaming Data](https://mlsanity.com/paper/2509.02840/) (2025)

## Abstract (arXiv)

This paper describes a new algorithm for computing a low-Tucker-rank approximation of a tensor. The method applies a randomized linear map to the tensor to obtain a sketch that captures the important directions within each mode, as well as the interactions among the modes. The sketch can be extracted from streaming or distributed data or with a single pass over the tensor, and it uses storage proportional to the degrees of freedom in the output Tucker approximation. The algorithm does not require a second pass over the tensor, although it can exploit another view to compute a superior approximation. The paper provides a rigorous theoretical guarantee on the approximation error. Extensive numerical experiments show that that the algorithm produces useful results that improve on the state of the art for streaming Tucker decomposition.