Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization

By John Wright, Arvind Ganesh, Shankar R. Rao, YiGang Peng, Yi Ma. Neural Information Processing Systems, 2009

1,441 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/017438e9f62834694a4ea85f87f48bfcbd0490d7

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Citations in the corpus

FlowWeb: Joint image set alignment by weaving consistent, pixel-wise correspondences (2015, background): “But instead of using a global, centered representation of the data like [43, 18, 31], our representation is defined on pairwise connections in the graph, like [35].”
Rank-Sparsity Incoherence for Matrix Decomposition (2009, methodology): “In addition to the assumptions of our random sparsity and random orthogonal models, [ 30 ] also requires that the non-zero entries of A? have independently chosen signs that are ±1 with equal probability, while the left and right singular vectors of B? are chosen independent of each other.”
Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset (2015, methodology): “t [40] can be considered as RMC using l1-norm loss function, the main diﬀerence lies in that in RMC problems the support of missing entries is given, whereas in RPCA corrupted entries are never known [335][360]. From a statistical learning viewpoint, RPCA is a typical unsupervised learning problem w”
Incremental gradient on the Grassmannian for online foreground and background separation in subsampled video (2012, methodology): “We can make this model more powerful by keeping a d dimensional subspace or affine set with d > 0 [21, 25, 28].”
A unified approach to salient object detection via low rank matrix recovery (2012, methodology): “Wright et al.[25] show that L and S can be perfectly recovered by Eqn.”
Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization (2014, methodology): “It has been shown in [3, 9, 10, 21, 44] that, under some suitable conditions, the solution to problem (1) can be found by solving the convex optimization problem:”
Weighted Schatten $p$ -Norm Minimization for Image Denoising and Background Subtraction (2015, methodology): “For example, the video clip captured by a static camera satisfies the “low rank + sparse” structure so that the background modeling can be conducted via LRMA [1], [2].”
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery (2018, methodology): “The RPCA problem was initially formulated by Wright et al. [68] with the theoretical guarantee to exactly recover the ground truth tensor from grossly corrupted one under certain assumptions [6].”
Signal Recovery on Graphs: Variation Minimization (2014, background): “The main difference is the assumption that all matrix elements are measurable but corrupted by outliers [35], [36].”
Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision (2016, background): “…a static scenario in background and with relatively small moving objects in foreground over a period, naturally resulting in its low-rank property; this inspires various effective techniques on background modeling and foreground object detection in recent years (Wright et al, 2009; Mu et al, 2011).”
Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization (2013, methodology): “The existing approaches based on the nuclear norm heuristic, such as singular value thresholding (SVT [17]), nuclear norm regularized least squares (NNLS [18]), and robust principal component analysis (Robust PCA [19]), have strong theoretical guarantees.”
Learning incoherent sparse and low-rank patterns from multiple tasks (2010, result): “Note that recent works in [Candès et al. 2009; Chandrasekaran et al. 2009; Wright et al. 2009] consider the problem of decomposing a given matrix into its underlying sparse component and low-rank component in a different setting: they study the theoretical condition under which such two components c”
Nuclear Norm Based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes (2014, background): “Fazel et al. [18, 19] found that the convex envelope of rank (X) is the nuclear norm of X, i.e.”
Randomized Matrix Decompositions using R (2016, methodology): “The PCP concept is mathematically sound, and has been applied successfully to many applications like video surveillance and face recognition (Wright, Ganesh, Rao, Peng, and Ma 2009).”
Multidimensional simultaneous random plus erratic noise attenuation and interpolation for seismic data by joint low-rank and sparse inversion (2015, methodology): “, the problem of separating a matrix into a sum of a low-rank component and a sparse component (Candès et al., 2009; Wright et al., 2009; Chandrasekaran et al., 2011).”
On the Complexity of Robust PCA and ℓ1-norm Low-Rank Matrix Approximation (2015, background): “Although robust PCA and its variants are widely believed to be NP-hard (see, e.g., [26, 39]), it has, to the best of our knowledge, never been proved rigorously.”
Saliency Detection by Multitask Sparsity Pursuit (2012, methodology): “Index Terms— Multifeature modeling, multitask learning, saliency detection, sparse and low rank.”
LR3M: Robust Low-Light Enhancement via Low-Rank Regularized Retinex Model (2020, methodology): “The accelerated proximal gradient approach is provided in [29], [30].”