Corpus ID: 128259446

Low-Rank Approximation from Communication Complexity

@article{Musco2019LowRankAF,
  title={Low-Rank Approximation from Communication Complexity},
  author={Cameron Musco and Christopher Musco and David P. Woodruff},
  journal={ArXiv},
  year={2019},
  volume={abs/1904.09841}
}
  • Cameron Musco, Christopher Musco, David P. Woodruff
  • Published 2019
  • Mathematics, Computer Science
  • ArXiv
  • In low-rank approximation with missing entries, given $A\in \mathbb{R}^{n\times n}$ and binary $W \in \{0,1\}^{n\times n}$, the goal is to find a rank-$k$ matrix $L$ for which: $$cost(L)=\sum_{i=1}^{n} \sum_{j=1}^{n}W_{i,j}\cdot (A_{i,j} - L_{i,j})^2\le OPT+\epsilon \|A\|_F^2,$$ where $OPT=\min_{rank-k\ \hat{L}}cost(\hat L)$. This problem is also known as matrix completion and, depending on the choice of $W$, captures low-rank plus diagonal decomposition, robust PCA, low-rank recovery from… CONTINUE READING

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