Non-negative matrix factorization with α-divergence
Pattern Recognition Letters
Computational Intelligence and Neuroscience - Advances in Nonnegative Matrix and Tensor Factorization
Non-negative matrix factorization: Ill-posedness and a geometric algorithm
Pattern Recognition
Discriminant nonnegative tensor factorization algorithms
IEEE Transactions on Neural Networks
Knowledge extraction with non-negative matrix factorization for text classification
IDEAL'09 Proceedings of the 10th international conference on Intelligent data engineering and automated learning
ICANNGA'09 Proceedings of the 9th international conference on Adaptive and natural computing algorithms
Nonlinear non-negative component analysis algorithms
IEEE Transactions on Image Processing
An effective method of pruning support vector machine classifiers
IEEE Transactions on Neural Networks
Projective nonnegative graph embedding
IEEE Transactions on Image Processing
Sequential coordinate-wise DNMF for face recognition
ICAISC'10 Proceedings of the 10th international conference on Artificial intelligence and soft computing: Part I
IEEE Transactions on Neural Networks
Manifold-respecting discriminant nonnegative matrix factorization
Pattern Recognition Letters
Towards unique solutions of non-negative matrix factorization problems by a determinant criterion
Digital Signal Processing
Kullback-Leibler divergence for nonnegative matrix factorization
ICANN'11 Proceedings of the 21th international conference on Artificial neural networks - Volume Part I
Algorithms for nonnegative matrix factorization with the β-divergence
Neural Computation
A multilevel approach for nonnegative matrix factorization
Journal of Computational and Applied Mathematics
Graph dual regularization non-negative matrix factorization for co-clustering
Pattern Recognition
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part II
Review article: Max-margin Non-negative Matrix Factorization
Image and Vision Computing
Efficient Nonnegative Matrix Factorization via projected Newton method
Pattern Recognition
Multistability of α-divergence based NMF algorithms
Computers & Mathematics with Applications
Solving non-negative matrix factorization by alternating least squares with a modified strategy
Data Mining and Knowledge Discovery
Measuring the degree of face familiarity based on extended NMF
ACM Transactions on Applied Perception (TAP)
Modified subspace Barzilai-Borwein gradient method for non-negative matrix factorization
Computational Optimization and Applications
Global Minima Analysis of Lee and Seung's NMF Algorithms
Neural Processing Letters
Discriminative Orthogonal Nonnegative matrix factorization with flexibility for data representation
Expert Systems with Applications: An International Journal
A convergent algorithm for orthogonal nonnegative matrix factorization
Journal of Computational and Applied Mathematics
Journal of Global Optimization
Global convergence of modified multiplicative updates for nonnegative matrix factorization
Computational Optimization and Applications
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Nonnegative matrix factorization (NMF) is useful to find basis information of nonnegative data. Currently, multiplicative updates are a simple and popular way to find the factorization. However, for the common NMF approach of minimizing the Euclidean distance between approximate and true values, no proof has shown that multiplicative updates converge to a stationary point of the NMF optimization problem. Stationarity is important as it is a necessary condition of a local minimum. This paper discusses the difficulty of proving the convergence. We propose slight modifications of existing updates and prove their convergence. Techniques invented in this paper may be applied to prove the convergence for other bound-constrained optimization problems.