Blind separation of positive sources by globally convergent gradient search
Neural Computation
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Learning Image Components for Object Recognition
The Journal of Machine Learning Research
Convergence Analysis of Non-Negative Matrix Factorization for BSS Algorithm
Neural Processing Letters
IEEE Transactions on Neural Networks
Graph Regularized Nonnegative Matrix Factorization for Data Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Multistability of α-divergence based NMF algorithms
Computers & Mathematics with Applications
A "nonnegative PCA" algorithm for independent component analysis
IEEE Transactions on Neural Networks
On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
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Lee and Seung proposed nonnegative matrix factorization (NMF) algorithms to decompose patterns and images for structure retrieving. The NMF algorithms have been applied to various optimization problems. However, it is difficult to prove the convergence of this class of learning algorithms. This paper presents the global minima analysis of the NMF algorithms. In the analysis, invariant set is constructed so that the non-divergence of the algorithms can be guaranteed in the set. Using the features of linear equation systems and their solutions, the fixed points and convergence properties of the update algorithms are discussed in detail. The analysis shows that, although the cost function is not convex in both A and X together, it is possible to obtain the global minima from the particular learning algorithms. For different initializations, simulations are presented to confirm the analysis results.