Image Analysis Using Multigrid Relaxation Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multigrid
SVD based initialization: A head start for nonnegative matrix factorization
Pattern Recognition
SIAM Journal on Matrix Analysis and Applications
ICMLA '08 Proceedings of the 2008 Seventh International Conference on Machine Learning and Applications
Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
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
On the Complexity of Nonnegative Matrix Factorization
SIAM Journal on Optimization
Non-negative matrix factorization with quasi-newton optimization
ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization
IEEE Transactions on Neural Networks
Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons
SIAM Journal on Scientific Computing
A convergent algorithm for orthogonal nonnegative matrix factorization
Journal of Computational and Applied Mathematics
Journal of Global Optimization
Hi-index | 7.29 |
Nonnegative matrix factorization (NMF), the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices, has been shown to be useful in many applications, such as text mining, image processing, and computational biology. In this paper, we explain how algorithms for NMF can be embedded into the framework of multilevel methods in order to accelerate their initial convergence. This technique can be applied in situations where data admit a good approximate representation in a lower dimensional space through linear transformations preserving nonnegativity. Several simple multilevel strategies are described and are experimentally shown to speed up significantly three popular NMF algorithms (alternating nonnegative least squares, multiplicative updates and hierarchical alternating least squares) on several standard image datasets.