# Projection-based QLP Algorithm for Efficiently Computing Low-Rank Approximation of Matrices

arXiv: https://arxiv.org/abs/2103.07245 · HTML: https://mlsanity.com/paper/2103.07245/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 56 references that are in the map.
- First posted on arXiv 12 Mar 2021.

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

- [Optimal CUR Matrix Decompositions](https://mlsanity.com/paper/1405.7910/) (2014)
- [Robust and computationally feasible community detection in the presence of arbitrary outlier nodes](https://mlsanity.com/paper/1404.6000/) (2014)
- [Subspace-Orbit Randomized Decomposition for Low-rank Matrix Approximation](https://mlsanity.com/paper/1804.00462/) (2018)
- [Randomized Nonnegative Matrix Factorization](https://mlsanity.com/paper/1711.02037/) (2017)
- [Multitask diffusion adaptation over networks with common latent representations](https://mlsanity.com/paper/1702.03614/) (2017)
- [An Alternating Direction Method with Increasing Penalty for Stable Principal Component Pursuit](https://mlsanity.com/paper/1309.6553/) (2013)
- [Adaptive Randomized Dimension Reduction on Massive Data](https://mlsanity.com/paper/1504.03183/) (2015)
- [Sampling and multilevel coarsening algorithms for fast matrix approximations](https://mlsanity.com/paper/1711.00439/) (2017)

## Abstract (arXiv)

Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is computationally prohibitive for large matrices. In this paper, we introduce a new algorithm termed Projection-based Partial QLP (PbP-QLP) that efficiently approximates the p-QLP with high accuracy. Fundamental in our work is the exploitation of randomization and in contrast to the p-QLP, PbP-QLP does not use the pivoting strategy. As such, PbP-QLP can harness modern computer architectures, even better than competing randomized algorithms. The efficiency and effectiveness of our proposed PbP-QLP algorithm are investigated through various classes of synthetic and real-world data matrices.