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 _2. We study other _p 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 study _p-regression, entrywise _p-low rank approximation, and versions of approximate matrix multiplication.

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Reproductions