# Algorithms for ℓp Low Rank Approximation

arXiv: https://arxiv.org/abs/1705.06730 · HTML: https://mlsanity.com/paper/1705.06730/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2017.

## Built on by (most cited first, 1 of 1)

- [On Subspace Approximation and Subset Selection in Fewer Passes by MCMC Sampling](https://mlsanity.com/paper/2103.11107/) (2021)

## Abstract (arXiv)

We consider the problem of approximating a given matrix by a low-rank matrix so as to minimize the entrywise ℓp-approximation error, for any p ≥ 1; the case p = 2 is the classical SVD problem. We obtain the first provably good approximation algorithms for this version of low-rank approximation that work for every value of p ≥ 1, including p = ∞. Our algorithms are simple, easy to implement, work well in practice, and illustrate interesting tradeoffs between the approximation quality, the running time, and the rank of the approximating matrix.