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
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
An accelerated gradient method for trace norm minimization
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
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
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
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
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
SIAM Journal on Scientific Computing
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
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
A fast tri-factorization method for low-rank matrix recovery and completion
Pattern Recognition
Learning spectral embedding via iterative eigenvalue thresholding
Proceedings of the 21st ACM international conference on Information and knowledge management
Robust Recovery of Subspace Structures by Low-Rank Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In recent years, matrix rank minimization problems have aroused considerable interests from machine learning, data mining and computer vision communities. All of these problems can be solved via their convex relaxations which minimize the trace norm instead of the rank of the matrix, and have to be solved iteratively and involve singular value decomposition (SVD) at each iteration. Therefore, those algorithms for trace norm minimization problems suffer from high computation cost of multiple SVDs. In this paper, we propose an efficient Matrix Bi-Factorization (MBF) method to approximate the original trace norm minimization problem and mitigate the computation cost of performing SVDs. The proposed MBF method can be used to address a wide range of low-rank matrix recovery and completion problems such as low-rank and sparse matrix decomposition (LRSD), low-rank representation (LRR) and low-rank matrix completion (MC). We also present three small scale matrix trace norm models for LRSD, LRR and MC problems, respectively. Moreover, we develop two concrete linearized proximal alternative optimization 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 MBF method comparing with the state-of-the-art trace norm minimization algorithms.