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Accelerated Alternating Projections for Robust Principal Component Analysis. (arXiv:1711.05519v1 [cs.IT])
来源于:arXiv
We study robust PCA for the fully observed setting, which is about separating
a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from
their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new
algorithm, termed accelerated alternating projections, is introduced for robust
PCA which accelerates existing alternating projections proposed in [Netrapalli,
Praneeth, et al., 2014]. Let $\boldsymbol{L}_k$ and $\boldsymbol{S}_k$ be the
current estimates of the low rank matrix and the sparse matrix, respectively.
The algorithm achieves significant acceleration by first projecting
$\boldsymbol{D}-\boldsymbol{S}_k$ onto a low dimensional subspace before
obtaining the new estimate of $\boldsymbol{L}$ via truncated SVD. Exact
recovery guarantee has been established which shows linear convergence of the
proposed algorithm. Empirical performance evaluations establish the advantage
of our algorithm over other state-of-the-art algorithms for robust PCA. 查看全文>>