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Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applications. (arXiv:1810.05186v1 [cs.LG])
来源于:arXiv
The heavy-tailed distributions of corrupted outliers and singular values of
all channels in low-level vision have proven effective priors for many
applications such as background modeling, photometric stereo and image
alignment. And they can be well modeled by a hyper-Laplacian. However, the use
of such distributions generally leads to challenging non-convex, non-smooth and
non-Lipschitz problems, and makes existing algorithms very slow for large-scale
applications. Together with the analytic solutions to lp-norm minimization with
two specific values of p, i.e., p=1/2 and p=2/3, we propose two novel bilinear
factor matrix norm minimization models for robust principal component analysis.
We first define the double nuclear norm and Frobenius/nuclear hybrid norm
penalties, and then prove that they are in essence the Schatten-1/2 and 2/3
quasi-norms, respectively, which lead to much more tractable and scalable
Lipschitz optimization problems. Our experimental analysis shows that both our
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