Computers and Operations Research
Document clustering based on non-negative matrix factorization
Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
SIAM Journal on Matrix Analysis and Applications
Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
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
On the convergence of the block nonlinear Gauss-Seidel method under convex constraints
Operations Research Letters
A multilevel approach for nonnegative matrix factorization
Journal of Computational and Applied Mathematics
Efficient Nonnegative Matrix Factorization via projected Newton method
Pattern Recognition
iVisClustering: An Interactive Visual Document Clustering via Topic Modeling
Computer Graphics Forum
Fast bregman divergence NMF using taylor expansion and coordinate descent
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Journal of Global Optimization
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Nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used for numerous applications, including text mining, computer vision, pattern discovery, and bioinformatics. A mathematical formulation for NMF appears as a nonconvex optimization problem, and various types of algorithms have been devised to solve the problem. The alternating nonnegative least squares (ANLS) framework is a block coordinate descent approach for solving NMF, which was recently shown to be theoretically sound and empirically efficient. In this paper, we present a novel algorithm for NMF based on the ANLS framework. Our new algorithm builds upon the block principal pivoting method for the nonnegativity-constrained least squares problem that overcomes a limitation of the active set method. We introduce ideas that efficiently extend the block principal pivoting method within the context of NMF computation. Our algorithm inherits the convergence property of the ANLS framework and can easily be extended to other constrained NMF formulations. Extensive computational comparisons using data sets that are from real life applications as well as those artificially generated show that the proposed algorithm provides state-of-the-art performance in terms of computational speed.