Relative Errors for Deterministic Low-Rank Matrix Approximations

@inproceedings{Ghashami2014RelativeEF,
  title={Relative Errors for Deterministic Low-Rank Matrix Approximations},
  author={Mina Ghashami and Jeff M. Phillips},
  booktitle={SODA},
  year={2014}
}
We consider processing an n × d matrix A in a stream with row-wise updates according to a recent algorithm called Frequent Directions (Liberty, KDD 2013). This algorithm maintains an ` × d matrix Q deterministically, processing each row in O(d`) time; the processing time can be decreased to O(d`) with a slight modification in the algorithm and a constant increase in space. Then for any unit vector x, the matrix Q satisfies 0 ≤ ‖Ax‖ − ‖Qx‖ ≤ ‖A‖F /`. We show that if one sets ` = dk + k/εe and… CONTINUE READING
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