Adaptive Sampling and Fast Low-Rank Matrix Approximation

  title={Adaptive Sampling and Fast Low-Rank Matrix Approximation},
  author={Amit Deshpande and Santosh Vempala},
  booktitle={Electronic Colloquium on Computational Complexity},
We prove that any real matrix A contains a subset of at most 4k/ + 2k log(k + 1) rows whose span “contains” a matrix of rank at most k with error only (1 + ) times the error of the best rank-k approximation of A. We complement it with an almost matching lower bound by constructing matrices where the span of any k/2 rows does not “contain” a relative (1 + )-approximation of rank k. Our existence result leads to an algorithm that finds such rank-k approximation in time O M k + k log k + (m + n) k… CONTINUE READING
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