• DOI:10.1145/2488608.2488620
Corpus ID: 53236615

Low rank approximation and regression in input sparsity time

@inproceedings{Clarkson2013LowRA,
  title={Low rank approximation and regression in input sparsity time},
  author={K. Clarkson and D. Woodruff},
  booktitle={STOC '13},
  year={2013}
}

K. Clarkson, D. Woodruff

Published in STOC '13 2013

Mathematics, Computer Science

We design a new distribution over poly(r ε^-1) x n matrices S so that for any fixed n x d matrix A of rank r, with probability at least 9/10, SAx₂ = (1 pm ε)Ax₂ simultaneously for all x ∈ R^d. Such a matrix S is called a <i>subspace embedding</i>. Furthermore, SA can be computed in O(nnz(A)) + ~O(r²ε^-2) time, where nnz(A) is the number of non-zero entries of A. This improves over all previous subspace embeddings, which required at… CONTINUE READING

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