# On GROUSE and Incremental SVD

arXiv: https://arxiv.org/abs/1307.5494 · HTML: https://mlsanity.com/paper/1307.5494/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2013.

## Built on by (most cited first, 3 of 3)

- [Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challenges](https://mlsanity.com/paper/2602.11378/) (2026)
- [A Federated Data Fusion-Based Prognostic Model for Applications with Multi-Stream Incomplete Signals](https://mlsanity.com/paper/2311.07474/) (2023)
- [History-aware adaptive reduced-order models via incremental singular value decomposition](https://mlsanity.com/paper/2605.28684/) (2026)

## Abstract (arXiv)

GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an incremental algorithm for identifying a subspace of Rn from a sequence of vectors in this subspace, where only a subset of components of each vector is revealed at each iteration. Recent analysis has shown that GROUSE converges locally at an expected linear rate, under certain assumptions. GROUSE has a similar flavor to the incremental singular value decomposition algorithm, which updates the SVD of a matrix following addition of a single column. In this paper, we modify the incremental SVD approach to handle missing data, and demonstrate that this modified approach is equivalent to GROUSE, for a certain choice of an algorithmic parameter.