Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
SIAM Journal on Optimization
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
Removing Multiplicative Noise by Douglas-Rachford Splitting Methods
Journal of Mathematical Imaging and Vision
Efficient Online and Batch Learning Using Forward Backward Splitting
The Journal of Machine Learning Research
Motion Segmentation in the Presence of Outlying, Incomplete, or Corrupted Trajectories
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Robust principal component analysis?
Journal of the ACM (JACM)
Fixed point and Bregman iterative methods for matrix rank minimization
Mathematical Programming: Series A and B
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
SIAM Journal on Scientific Computing
Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods
SIAM Journal on Matrix Analysis and Applications
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations
SIAM Journal on Optimization
Journal of Mathematical Imaging and Vision
Robust Recovery of Subspace Structures by Low-Rank Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Given a set of corrupted data drawn from a union of multiple subspace, the subspace recovery problem is to segment the data into their respective subspace and to correct the possible noise simultaneously. Recently, it is discovered that the task can be characterized, both theoretically and numerically, by solving a matrix nuclear-norm and a 驴2,1-mixed norm involved convex minimization problems. The minimization model actually has separable structure in both the objective function and constraint; it thus falls into the framework of the augmented Lagrangian alternating direction approach. In this paper, we propose and investigate an augmented Lagrangian algorithm. We split the augmented Lagrangian function and minimize the subproblems alternatively with one variable by fixing the other one. Moreover, we linearize the subproblem and add a proximal point term to easily derive the closed-form solutions. Global convergence of the proposed algorithm is established under some technical conditions. Extensive experiments on the simulated and the real data verify that the proposed method is very effective and faster than the sate-of-the-art algorithm LRR.