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

Graham Cormode, Charlie Dickens, David P. Woodruff

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