# Leveraging Well-Conditioned Bases: Streaming & Distributed Summaries in Minkowski p-Norms

arXiv: https://arxiv.org/abs/1807.02571 · HTML: https://mlsanity.com/paper/1807.02571/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2018.

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

- [On Socially Fair Low-Rank Approximation and Column Subset Selection](https://mlsanity.com/paper/2412.06063/) (2024)
- [One-pass additive-error subset selection for ℓp subspace approximation](https://mlsanity.com/paper/2204.12073/) (2022)
- [On Subspace Approximation and Subset Selection in Fewer Passes by MCMC Sampling](https://mlsanity.com/paper/2103.11107/) (2021)
- [Deterministic Coreset for Lp Subspace](https://mlsanity.com/paper/2601.00361/) (2026)

## Abstract (arXiv)

Work on approximate linear algebra has led to efficient distributed and streaming algorithms for problems such as approximate matrix multiplication, low rank approximation, and regression, primarily for the Euclidean norm ℓ2. We study other ℓp norms, which are more robust for p < 2, and can be used to find outliers for p > 2. Unlike previous algorithms for such norms, we give algorithms that are (1) deterministic, (2) work simultaneously for every p ≥ 1, including p = ∞, and (3) can be implemented in both distributed and streaming environments. We apply our results to ℓp-regression, entrywise ℓ1-low rank approximation, and approximate matrix multiplication.