Projected gradient methods for linearly constrained problems
Mathematical Programming: Series A and B
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
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
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
Extended SMART algorithms for non-negative matrix factorization
ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
On the convergence of the block nonlinear Gauss-Seidel method under convex constraints
Operations Research Letters
On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization
IEEE Transactions on Neural Networks
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Rank-one residue iteration (RRI) is a recently developed block coordinate method for nonnegative matrix factorization (NMF). Numerical results show that the decomposed matrices generated by RRI method may have several columns, which are zero vectors. In this paper, by studying two special kinds of quadratic programming, we develop two block coordinate methods for NMF, rank-two residue iteration (RTRI) method and rank-two modified residue iteration (RTMRI) method. In the two algorithms, the exact solution of the subproblem can be obtained directly. We also provide that the consequence generated by our proposed algorithms can converge to a stationary point. Numerical results show that the RTRI method and the RTMRI method can yield better solutions, especially RTMRI method can remedy the limitation of the RRI method.