Corpus ID: 51679337

A PTAS for $\ell_p$-Low Rank Approximation

@inproceedings{Ban2018APF,
  title={A PTAS for \$\ell_p\$-Low Rank Approximation},
  author={Frank Ban and Vijay Bhattiprolu and Karl Bringmann and Pavel Kolev and Euiwoong Lee and David P. Woodruff},
  booktitle={SODA 2019},
  year={2018}
}
  • Frank Ban, Vijay Bhattiprolu, +3 authors David P. Woodruff
  • Published in SODA 2018
  • Computer Science, Mathematics
  • A number of recent works have studied algorithms for entrywise $\ell_p$-low rank approximation, namely algorithms which given an $n \times d$ matrix $A$ (with $n \geq d$), output a rank-$k$ matrix $B$ minimizing $\|A-B\|_p^p=\sum_{i,j} |A_{i,j} - B_{i,j}|^p$. We show the following: On the algorithmic side, for $p \in (0,2)$, we give the first $n^{\text{poly}(k/\epsilon)}$ time $(1+\epsilon)$-approximation algorithm. For $p = 0$, there are various problem formulations, a common one being the… CONTINUE READING

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    2
    Twitter Mentions

    Citations

    Publications citing this paper.

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 74 REFERENCES

    On Two Segmentation Problems

    VIEW 6 EXCERPTS
    HIGHLY INFLUENTIAL

    Low rank approximation with entrywise l1-norm error

    VIEW 8 EXCERPTS

    Hypercontractivity, sum-of-squares proofs, and their applications

    VIEW 13 EXCERPTS
    HIGHLY INFLUENTIAL

    On the Complexity of k-SAT

    VIEW 9 EXCERPTS
    HIGHLY INFLUENTIAL

    Inapproximability of Matrix p→q Norms

    VIEW 4 EXCERPTS

    On the Complexity of Robust PCA and ℓ1-norm Low-Rank Matrix Approximation

    VIEW 8 EXCERPTS
    HIGHLY INFLUENTIAL

    On Low Rank Approximation of Binary Matrices

    VIEW 10 EXCERPTS
    HIGHLY INFLUENTIAL