Matrix analysis
Computers and Operations Research
Pattern Recognition Letters
Atomic Decomposition by Basis Pursuit
SIAM Review
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Document clustering based on non-negative matrix factorization
Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Orthogonal nonnegative matrix t-factorizations for clustering
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
Nonnegative matrix factorization via rank-one downdate
Proceedings of the 25th international conference on Machine learning
Low-Dimensional Polytope Approximation and Its Applications to Nonnegative Matrix Factorization
SIAM Journal on Scientific Computing
Computing non-negative tensor factorizations
Optimization Methods & Software - Mathematical programming in data mining and machine learning
SIAM Journal on Matrix Analysis and Applications
Computational Intelligence and Neuroscience - Advances in Nonnegative Matrix and Tensor Factorization
Unsupervised Multiway Data Analysis: A Literature Survey
IEEE Transactions on Knowledge and Data Engineering
Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Block-Iterative Algorithms for Non-negative Matrix Approximation
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Bayesian Non-negative Matrix Factorization
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Distance Metric Learning for Large Margin Nearest Neighbor Classification
The Journal of Machine Learning Research
Detect and track latent factors with online nonnegative matrix factorization
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Tensor Decompositions and Applications
SIAM Review
Convex and Semi-Nonnegative Matrix Factorizations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using underapproximations for sparse nonnegative matrix factorization
Pattern Recognition
Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
On the Complexity of Nonnegative Matrix Factorization
SIAM Journal on Optimization
Graph Regularized Nonnegative Matrix Factorization for Data Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Sequential coordinate-wise algorithm for the non-negative least squares problem
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
A multilevel approach for nonnegative matrix factorization
Journal of Computational and Applied Mathematics
Non-negative matrix factorization with quasi-newton optimization
ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
On the convergence of the block nonlinear Gauss-Seidel method under convex constraints
Operations Research Letters
On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization
IEEE Transactions on Neural Networks
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
Nonnegative matrix and tensor factorizations, least squares problems, and applications
Nonnegative matrix and tensor factorizations, least squares problems, and applications
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We review algorithms developed for nonnegative matrix factorization (NMF) and nonnegative tensor factorization (NTF) from a unified view based on the block coordinate descent (BCD) framework. NMF and NTF are low-rank approximation methods for matrices and tensors in which the low-rank factors are constrained to have only nonnegative elements. The nonnegativity constraints have been shown to enable natural interpretations and allow better solutions in numerous applications including text analysis, computer vision, and bioinformatics. However, the computation of NMF and NTF remains challenging and expensive due the constraints. Numerous algorithmic approaches have been proposed to efficiently compute NMF and NTF. The BCD framework in constrained non-linear optimization readily explains the theoretical convergence properties of several efficient NMF and NTF algorithms, which are consistent with experimental observations reported in literature. In addition, we discuss algorithms that do not fit in the BCD framework contrasting them from those based on the BCD framework. With insights acquired from the unified perspective, we also propose efficient algorithms for updating NMF when there is a small change in the reduced dimension or in the data. The effectiveness of the proposed updating algorithms are validated experimentally with synthetic and real-world data sets.