Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Csiszár’s divergences for non-negative matrix factorization: family of new algorithms
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Accelerating the EMML algorithm and related iterative algorithms by rescaled block-iterative methods
IEEE Transactions on Image Processing
Journal of VLSI Signal Processing Systems
Non-negative matrix factorization with α-divergence
Pattern Recognition Letters
Nonnegative matrix factorization with quadratic programming
Neurocomputing
Computational Intelligence and Neuroscience - Advances in Nonnegative Matrix and Tensor Factorization
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
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
Sparse non-negative tensor factorization using columnwise coordinate descent
Pattern Recognition
A multilevel approach for nonnegative matrix factorization
Journal of Computational and Applied Mathematics
Efficient Nonnegative Matrix Factorization via projected Newton method
Pattern Recognition
Solving non-negative matrix factorization by alternating least squares with a modified strategy
Data Mining and Knowledge Discovery
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
Modified subspace Barzilai-Borwein gradient method for non-negative matrix factorization
Computational Optimization and Applications
Journal of Global Optimization
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Non-negative matrix factorization (NMF) is an emerging method with wide spectrum of potential applications in data analysis, feature extraction and blind source separation. Currently, most applications use relative simple multiplicative NMF learning algorithms which were proposed by Lee and Seung, and are based on minimization of the Kullback-Leibler divergence and Frobenius norm. Unfortunately, these algorithms are relatively slow and often need a few thousands of iterations to achieve a local minimum. In order to increase a convergence rate and to improve performance of NMF, we proposed to use a more general cost function: so-called Amari alpha divergence. Taking into account a special structure of the Hessian of this cost function, we derived a relatively simple second-order quasi-Newton method for NMF. The validity and performance of the proposed algorithm has been extensively tested for blind source separation problems, both for signals and images. The performance of the developed NMF algorithm is illustrated for separation of statistically dependent signals and images from their linear mixtures.