Robust blind source separation by beta divergence
Neural Computation
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Local Non-Negative Matrix Factorization as a Visual Representation
ICDL '02 Proceedings of the 2nd International Conference on Development and Learning
Introducing a weighted non-negative matrix factorization for image classification
Pattern Recognition Letters
Divergence function, duality, and convex analysis
Neural Computation
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Nonnegative features of spectro-temporal sounds for classification
Pattern Recognition Letters
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
Choosing parameters in block-iterative or ordered subset reconstruction algorithms
IEEE Transactions on Image Processing
Gradient-based manipulation of nonparametric entropy estimates
IEEE Transactions on Neural Networks
A compact factored representation of heterogeneous subsurface scattering
ACM SIGGRAPH 2006 Papers
Non-negative matrix factorization with α-divergence
Pattern Recognition Letters
Nonnegative matrix factorization with quadratic programming
Neurocomputing
On α-divergence based nonnegative matrix factorization for clustering cancer gene expression data
Artificial Intelligence in Medicine
Novel Multi-layer Non-negative Tensor Factorization with Sparsity Constraints
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part II
Regularized Alternating Least Squares Algorithms for Non-negative Matrix/Tensor Factorization
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks, Part III
Sparse Super Symmetric Tensor Factorization
Neural Information Processing
Data Clustering with Semi-binary Nonnegative Matrix Factorization
ICAISC '08 Proceedings of the 9th international conference on Artificial Intelligence and Soft Computing
Fast and Efficient Algorithms for Nonnegative Tucker Decomposition
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks, Part II
Computational Intelligence and Neuroscience - Advances in Nonnegative Matrix and Tensor Factorization
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
IEEE Transactions on Neural Networks
Towards unique solutions of non-negative matrix factorization problems by a determinant criterion
Digital Signal Processing
A convergent algorithm for orthogonal nonnegative matrix factorization
Journal of Computational and Applied Mathematics
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In this paper we derive a family of new extended SMART (Simultaneous Multiplicative Algebraic Reconstruction Technique) algorithms for Non-negative Matrix Factorization (NMF). The proposed algorithms are characterized by improved efficiency and convergence rate and can be applied for various distributions of data and additive noise. Information theory and information geometry play key roles in the derivation of new algorithms. We discuss several loss functions used in information theory which allow us to obtain generalized forms of multiplicative NMF learning adaptive algorithms. We also provide flexible and relaxed forms of the NMF algorithms to increase convergence speed and impose an additional constraint of sparsity. The scope of these results is vast since discussed generalized divergence functions include a large number of useful loss functions such as the Amari α– divergence, Relative entropy, Bose-Einstein divergence, Jensen-Shannon divergence, J-divergence, Arithmetic-Geometric (AG) Taneja divergence, etc. We applied the developed algorithms successfully to Blind (or semi blind) Source Separation (BSS) where sources may be generally statistically dependent, however are subject to additional constraints such as nonnegativity and sparsity. Moreover, we applied a novel multilayer NMF strategy which improves performance of the most proposed algorithms.