# Fast and Accurate SVD-Type Updating in Streaming Data

arXiv: https://arxiv.org/abs/2509.02840 · HTML: https://mlsanity.com/paper/2509.02840/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 2 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [SVDiff: Compact Parameter Space for Diffusion Fine-Tuning](https://mlsanity.com/paper/2303.11305/) (2023)
- [Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition](https://mlsanity.com/paper/1504.05477/) (2015)
- [Low-Rank Tucker Approximation of a Tensor From Streaming Data](https://mlsanity.com/paper/1904.10951/) (2019)
- [Stochastic gradient descent for streaming linear and rectified linear systems with adversarial corruptions](https://mlsanity.com/paper/2403.01204/) (2024)
- [Algorithm XXX: SC-SR1: Matlab software for solving shape-changing L-SR1 trust-region subproblems](https://mlsanity.com/paper/1607.03533/) (2016)
- [Large-scale Optimization with Linear Equality Constraints using Reduced Compact Representation](https://mlsanity.com/paper/2101.11048/) (2021)
- [Efficient Algorithms for Regularized Nonnegative Scale-invariant Low-rank Approximation Models](https://mlsanity.com/paper/2403.18517/) (2024)

## Abstract (arXiv)

For a datastream, the change over a short interval is often of low rank. For high throughput information arranged in matrix format, recomputing an optimal SVD approximation after each step is typically prohibitive. Instead, incremental and truncated updating strategies are used, which may not scale for large truncation ranks. Therefore, we propose a set of efficient new algorithms that update a bidiagonal factorization, and which are similarly accurate as the SVD methods. In particular, we develop a compact Householder-type algorithm that decouples a sparse part from a low-rank update and has about half the memory requirements of standard bidiagonalization methods. A second algorithm based on Givens rotations has only about 10 flops per rotation and scales quadratically with the problem size, compared to a typical cubic scaling. The algorithm is therefore effective for processing high-throughput updates, as we demonstrate in tracking large subspaces of recommendation systems and networks, and when compared to well known software such as LAPACK or the incremental SVD.