منابع مشابه
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...
متن کاملSupplementary Material of Exact Recoverability of Robust PCA via Outlier Pursuit with Tight Recovery Bounds
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...
متن کاملThresholding based Efficient Outlier Robust PCA
We consider the problem of outlier robust PCA (OR-PCA) where the goal is to recover principal directions despite the presence of outlier data points. That is, given a data matrix M∗, where (1 − α) fraction of the points are noisy samples from a low-dimensional subspace while α fraction of the points can be arbitrary outliers, the goal is to recover the subspace accurately. Existing results for ...
متن کاملA Unified Framework for Outlier-Robust PCA-like Algorithms
We propose a unified framework for making a wide range of PCA-like algorithms – including the standard PCA, sparse PCA and non-negative sparse PCA, etc. – robust when facing a constant fraction of arbitrarily corrupted outliers. Our analysis establishes solid performance guarantees of the proposed framework: its estimation error is upper bounded by a term depending on the intrinsic parameters o...
متن کاملRobust PCA for skewed data and its outlier map
The outlier sensitivity of classical principal component analysis (PCA) has spurred the development of robust techniques. Existing robust PCA methods like ROBPCA work best if the non-outlying data have an approximately symmetric distribution. When the original variables are skewed, too many points tend to be flagged as outlying. A robust PCA method is developed which is also suitable for skewed...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2012
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2011.2173156