Practical low-rank matrix approximation under robust L1-norm

By Yinqiang Zheng, Guangcan Liu, Shigeki Sugimoto, Shuicheng Yan, Masatoshi Okutomi. 2012

218 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Efficient $l_{1}$ -Norm-Based Low-Rank Matrix Approximations for Large-Scale Problems Using Alternating Rectified Gradient Method (2015, methodology): “and Wl1-ARGD) in Sections IV and V, and the performances were compared with those of other methods that can handle missing data (ALADM-MC, which is a matrix completion (MC) version of ALADM [8], Regl1-ALM [10]).”
On the Complexity of Robust PCA and ℓ1-norm Low-Rank Matrix Approximation (2015, background): “Adding weights in the objective function, that is, minimizing ∑ i,j Wij(M − UV )2ij for some nonnegative weight matrix W ∈ Rm×n+ , allows to take into account different confidence levels among the entries of the input data M [15], or take into account missing entries (corresponding to zero entries…”
Weighted Schatten $p$ -Norm Minimization for Image Denoising and Background Subtraction (2015, methodology): “Also, the occluded or corrupted faces can be recovered by exploiting the low rank nature of matrix constructed by human facial images [3], [4], [5].”
Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision (2016, methodology): “…facial images can be modeled as reflections of a Lambertian object and approximated by a low dimensional linear subspace; this low rank nature leads to a proper reconstruction of a face model from occluded/corrupted face images (De La Torre and Black, 2003; Liu et al, 2010; Zheng et al, 2012).”
Unifying Nuclear Norm and Bilinear Factorization Approaches for Low-Rank Matrix Decomposition (2013, background): “[41] extended [15] by adding a nuclear norm regularizer to V and the orthogonality constraints in U found in [5] for structure from motion.”
Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset (2015, methodology): “d objective in Equation 166. Experimental results [458] are presented on Structure from Motion (SFM) but not on background/foreground separation. Algorithm for solving PLRMF (RegL1-ALM): Zheng et al. [458] developed a scalable ﬁrst-order optimization algorithm to solve the regularized formulation on”
Weighted Nuclear Norm Minimization with Application to Image Denoising (2014, background): “For instance, the low rank nature of matrix formed by human facial images allows us to reconstruct the occluded/corrupted faces [8, 20, 30].”