Supplementary Material of Exact Recoverability of Robust PCA via Outlier Pursuit with Tight Recovery Bounds
نویسندگان
چکیده
Theorem 1 (Exact Recovery of Outlier Pursuit). Suppose m = Θ(n), Range(L0) = Range(PI⊥ 0 L0), and [S0]:j 6∈ Range(L0) for ∀j ∈ I0. Then any solution (L0+H,S0−H) to Outlier Pursuit (1) with λ = 1/ √ log n exactly recovers the column space of L0 and the column support of S0 with a probability at least 1 − cn−10, if the column support I0 of S0 is uniformly distributed among all sets of cardinality s and rank(L0) ≤ ρr n(2)
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Exact Recoverability of Robust PCA via Outlier Pursuit with Tight Recovery Bounds
Subspace recovery from noisy or even corrupted data is critical for various applications in machine learning and data analysis. To detect outliers, Robust PCA (R-PCA) via Outlier Pursuit was proposed and had found many successful applications. However, the current theoretical analysis on Outlier Pursuit only shows that it succeeds when the sparsity of the corruption matrix is of O(n/r), where n...
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