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
A multilevel approach for nonnegative matrix factorization
Journal of Computational and Applied Mathematics
Efficient Nonnegative Matrix Factorization via projected Newton method
Pattern Recognition
Non-negative residual matrix factorization: problem definition, fast solutions, and applications
Statistical Analysis and Data Mining
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
Hybrid online non-negative matrix factorization for clustering of documents
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part I
Spatially correlated nonnegative matrix factorization for image analysis
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Fast rank-2 nonnegative matrix factorization for hierarchical document clustering
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
A convergent algorithm for orthogonal nonnegative matrix factorization
Journal of Computational and Applied Mathematics
Journal of Global Optimization
Kernel clustering using a hybrid memetic algorithm
Natural Computing: an international journal
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Nonnegative Matrix Factorization (NMF) is a dimension reduction method that has been widely used for various tasks including text mining, pattern analysis, clustering, and cancer class discovery. The mathematical formulation for NMF appears as a non-convex 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 some limitations of active set methods. We introduce ideas to efficiently extend the block principal pivoting method within the context of NMF computation. Our algorithm inherits the convergence theory of the ANLS framework and can easily be extended to other constrained NMF formulations. Comparisons of algorithms using datasets that are from real life applications as well as those artificially generated show that the proposed new algorithm outperforms existing ones in computational speed.