A Multibody Factorization Method for Independently Moving Objects
International Journal of Computer Vision
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Acquiring Linear Subspaces for Face Recognition under Variable Lighting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
SIAM Journal on Computing
Orthogonal nonnegative matrix t-factorizations for clustering
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sparsity preserving projections with applications to face recognition
Pattern Recognition
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration
SIAM Journal on Imaging Sciences
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
SIAM Journal on Matrix Analysis and Applications
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Matrix Completion from Noisy Entries
The Journal of Machine Learning Research
Decomposing background topics from keywords by principal component pursuit
CIKM '10 Proceedings of the 19th ACM international conference on Information and knowledge management
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Robust Low-Rank Subspace Segmentation with Semidefinite Guarantees
ICDMW '10 Proceedings of the 2010 IEEE International Conference on Data Mining Workshops
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
Fast density-weighted low-rank approximation spectral clustering
Data Mining and Knowledge Discovery
Integrating low-rank and group-sparse structures for robust multi-task learning
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Learning Spectral Embedding for Semi-supervised Clustering
ICDM '11 Proceedings of the 2011 IEEE 11th International Conference on Data Mining
Graph dual regularization non-negative matrix factorization for co-clustering
Pattern Recognition
A closed form solution to robust subspace estimation and clustering
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Accelerated low-rank visual recovery by random projection
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
TILT: Transform Invariant Low-Rank Textures
International Journal of Computer Vision
Real-Time Discriminative Background Subtraction
IEEE Transactions on Image Processing
Bayesian Robust Principal Component Analysis
IEEE Transactions on Image Processing
Semi-supervised learning with mixed knowledge information
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Multi-task low-rank affinity pursuit for image segmentation
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Latent Low-Rank Representation for subspace segmentation and feature extraction
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
A Neural Network Approach to the Frictionless Grasping Problem
Journal of Intelligent and Robotic Systems
A Theoretical Approach of an Intelligent Robot Gripper to Grasp Polygon Shaped Objects
Journal of Intelligent and Robotic Systems
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In recent years, matrix rank minimization problems have received a significant amount of attention in machine learning, data mining and computer vision communities. And these problems can be solved by a convex relaxation of the rank minimization problem which minimizes the nuclear norm instead of the rank of the matrix, and has to be solved iteratively and involves singular value decomposition (SVD) at each iteration. Therefore, those algorithms for nuclear norm minimization problems suffer from high computation cost of multiple SVDs. In this paper, we propose a Fast Tri-Factorization (FTF) method to approximate the nuclear norm minimization problem and mitigate the computation cost of performing SVDs. The proposed FTF method can be used to reliably solve a wide range of low-rank matrix recovery and completion problems such as robust principal component analysis (RPCA), low-rank representation (LRR) and low-rank matrix completion (MC). We also present three specific models for RPCA, LRR and MC problems, respectively. Moreover, we develop two alternating direction method (ADM) based iterative algorithms for solving the above three problems. Experimental results on a variety of synthetic and real-world data sets validate the efficiency, robustness and effectiveness of our FTF method comparing with the state-of-the-art nuclear norm minimization algorithms.