# Online high rank matrix completion

arXiv: https://arxiv.org/abs/2002.08934 · HTML: https://mlsanity.com/paper/2002.08934/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2020.

## Built on by (most cited first, 4 of 4)

- [Beyond the Signs: Nonparametric Tensor Completion via Sign Series](https://mlsanity.com/paper/2102.00384/) (2021)
- [Nonlinear matrix recovery using optimization on the Grassmann manifold](https://mlsanity.com/paper/2109.06095/) (2021)
- [Tailed Low-Rank Matrix Factorization for Similarity Matrix Completion](https://mlsanity.com/paper/2409.19550/) (2024)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)

## Abstract (arXiv)

Recent advances in matrix completion enable data imputation in full-rank matrices by exploiting low dimensional (nonlinear) latent structure. In this paper, we develop a new model for high rank matrix completion (HRMC), together with batch and online methods to fit the model and out-of-sample extension to complete new data. The method works by (implicitly) mapping the data into a high dimensional polynomial feature space using the kernel trick; importantly, the data occupies a low dimensional subspace in this feature space, even when the original data matrix is of full-rank. We introduce an explicit parametrization of this low dimensional subspace, and an online fitting procedure, to reduce computational complexity compared to the state of the art. The online method can also handle streaming or sequential data and adapt to non-stationary latent structure. We provide guidance on the sampling rate required these methods to succeed. Experimental results on synthetic data and motion capture data validate the performance of the proposed methods.