Leveraging well-conditioned bases : streaming and distributed summaries in Minkowski p-norms

Abstract

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 p2. 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 study ℓp-regression, entrywise ℓp-low rank approximation, and versions of approximate matrix multiplication