Using underapproximations for sparse nonnegative matrix factorization
Pattern Recognition
Data transformations and representations for computation and visualization
Information Visualization
Sparse nonnegative matrix factorization for protein sequence motif discovery
Expert Systems with Applications: An International Journal
Fast coordinate descent methods with variable selection for non-negative matrix factorization
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
IWANN'11 Proceedings of the 11th international conference on Artificial neural networks conference on Advances in computational intelligence - Volume Part II
Using population based algorithms for initializing nonnegative matrix factorization
ICSI'11 Proceedings of the Second international conference on Advances in swarm intelligence - Volume Part II
Kullback-Leibler divergence for nonnegative matrix factorization
ICANN'11 Proceedings of the 21th international conference on Artificial neural networks - Volume Part I
A multilevel approach for nonnegative matrix factorization
Journal of Computational and Applied Mathematics
Sparse nonnegative matrix factorization with ℓ0-constraints
Neurocomputing
Graph dual regularization non-negative matrix factorization for co-clustering
Pattern Recognition
Nesterov's iterations for NMF-Based supervised classification of texture patterns
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Efficient Nonnegative Matrix Factorization via projected Newton method
Pattern Recognition
EigenBot: foiling spamming botnets with matrix algebra
Proceedings of the ACM SIGKDD Workshop on Intelligence and Security Informatics
Fast bregman divergence NMF using taylor expansion and coordinate descent
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons
SIAM Journal on Scientific Computing
Discrete Eckart-Young Theorem for Integer Matrices
SIAM Journal on Matrix Analysis and Applications
A collective NMF method for detecting protein functional module from multiple data sources
Proceedings of the ACM Conference on Bioinformatics, Computational Biology and Biomedicine
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part I
Regularized nonnegative shared subspace learning
Data Mining and Knowledge Discovery
Solving non-negative matrix factorization by alternating least squares with a modified strategy
Data Mining and Knowledge Discovery
Fast rank-2 nonnegative matrix factorization for hierarchical document clustering
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Low-rank matrix completion using alternating minimization
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Nonnegative Least-Squares Methods for the Classification of High-Dimensional Biological Data
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A convergent algorithm for orthogonal nonnegative matrix factorization
Journal of Computational and Applied Mathematics
Journal of Global Optimization
Nonnegative rank factorization--a heuristic approach via rank reduction
Numerical Algorithms
Computational Optimization and Applications
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Nonnegative matrix factorization (NMF) determines a lower rank approximation of a matrix $A \in \mathbb{R}^{m \times n} \approx WH$ where an integer $k \ll \min(m,n)$ is given and nonnegativity is imposed on all components of the factors $W \in \mathbb{R}^{m \times k}$ and $H \in \mathbb{R}^{k \times n}$. NMF has attracted much attention for over a decade and has been successfully applied to numerous data analysis problems. In applications where the components of the data are necessarily nonnegative, such as chemical concentrations in experimental results or pixels in digital images, NMF provides a more relevant interpretation of the results since it gives nonsubtractive combinations of nonnegative basis vectors. In this paper, we introduce an algorithm for NMF based on alternating nonnegativity constrained least squares (NMF/ANLS) and the active set-based fast algorithm for nonnegativity constrained least squares with multiple right-hand side vectors, and we discuss its convergence properties and a rigorous convergence criterion based on the Karush-Kuhn-Tucker (KKT) conditions. In addition, we also describe algorithms for sparse NMFs and regularized NMF. We show how we impose a sparsity constraint on one of the factors by $L_1$-norm minimization and discuss its convergence properties. Our algorithms are compared to other commonly used NMF algorithms in the literature on several test data sets in terms of their convergence behavior.