# A Perturbation Bound on the Subspace Estimator from Canonical Projections

arXiv: https://arxiv.org/abs/2206.14278 · HTML: https://mlsanity.com/paper/2206.14278/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 26 references that are in the map.
- First posted on arXiv 28 Jun 2022.

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

- [A Characterization of Deterministic Sampling Patterns for Low-Rank Matrix Completion](https://mlsanity.com/paper/1503.02596/) (2015)
- [Preference Completion: Large-scale Collaborative Ranking from Pairwise Comparisons](https://mlsanity.com/paper/1507.04457/) (2015)
- [Tensor Methods for Nonlinear Matrix Completion](https://mlsanity.com/paper/1804.10266/) (2018)
- [Fundamental Conditions for Low-CP-Rank Tensor Completion](https://mlsanity.com/paper/1703.10740/) (2017)
- [Deterministic Conditions for Subspace Identifiability from Incomplete Sampling](https://mlsanity.com/paper/1410.0633/) (2014)
- [Deterministic and Probabilistic Conditions for Finite Completability of Low-rank Multi-View Data](https://mlsanity.com/paper/1701.00737/) (2017)
- [On Deterministic Sampling Patterns for Robust Low-Rank Matrix Completion](https://mlsanity.com/paper/1712.01628/) (2017)
- [Mixture Matrix Completion](https://mlsanity.com/paper/1808.00616/) (2018)

## Abstract (arXiv)

This paper derives a perturbation bound on the optimal subspace estimator obtained from a subset of its canonical projections contaminated by noise. This fundamental result has important implications in matrix completion, subspace clustering, and related problems.