# High Rank Matrix Completion via Grassmannian Proxy Fusion

arXiv: https://arxiv.org/abs/2602.02565 · HTML: https://mlsanity.com/paper/2602.02565/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 57 references that are in the map.
- First posted on arXiv 30 Jan 2026.

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

- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [A Shrinkage Principle for Heavy-Tailed Data: High-Dimensional Robust Low-Rank Matrix Recovery](https://mlsanity.com/paper/1603.08315/) (2016)
- [Algebraic Variety Models for High-Rank Matrix Completion](https://mlsanity.com/paper/1703.09631/) (2017)
- [Sketched Subspace Clustering](https://mlsanity.com/paper/1707.07196/) (2017)
- [Theoretical Analysis of Sparse Subspace Clustering with Missing Entries](https://mlsanity.com/paper/1801.00393/) (2018)
- [Low-rank matrix completion and denoising under Poisson noise](https://mlsanity.com/paper/1907.05325/) (2019)
- [Robust Low-rank Matrix Completion via an Alternating Manifold Proximal Gradient Continuation Method](https://mlsanity.com/paper/2008.07740/) (2020)
- [Completing Any Low-rank Matrix, Provably](https://mlsanity.com/paper/1306.2979/) (2013)

## Abstract (arXiv)

This paper approaches high-rank matrix completion (HRMC) by filling missing entries in a data matrix where columns lie near a union of subspaces, clustering these columns, and identifying the underlying subspaces. Current methods often lack theoretical support, produce uninterpretable results, and require more samples than theoretically necessary. We propose clustering incomplete vectors by grouping proxy subspaces and minimizing two criteria over the Grassmannian: (a) the chordal distance between each point and its corresponding subspace and (b) the geodesic distances between subspaces of all data points. Experiments on synthetic and real datasets demonstrate that our method performs comparably to leading methods in high sampling rates and significantly better in low sampling rates, thus narrowing the gap to the theoretical sampling limit of HRMC.