Multiplicative updates for non-negative projections
Neurocomputing
Projective Nonnegative Matrix Factorization with α -Divergence
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part I
Multiresolution approach in computing NTF
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Linear and nonlinear projective nonnegative matrix factorization
IEEE Transactions on Neural Networks
Projective nonnegative graph embedding
IEEE Transactions on Image Processing
Automatic rank determination in projective nonnegative matrix factorization
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Quadratic nonnegative matrix factorization
Pattern Recognition
Subclass discriminant Nonnegative Matrix Factorization for facial image analysis
Pattern Recognition
Adaptive multiplicative updates for projective nonnegative matrix factorization
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
Convergent Projective Non-negative Matrix Factorization with Kullback-Leibler Divergence
Pattern Recognition Letters
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In image compression and feature extraction, linear expansions are standardly used. It was recently pointed out by Lee and Seung that the positivity or non-negativity of a linear expansion is a very powerful constraint, that seems to lead to sparse representations for the images. Their technique, called Non-negative Matrix Factorization (NMF), was shown to be a useful technique in approximating high dimensional data where the data are comprised of non-negative components. We propose here a new variant of the NMF method for learning spatially localized, sparse, part-based subspace representations of visual patterns. The algorithm is based on positively constrained projections and is related both to NMF and to the conventional SVD or PCA decomposition. Two iterative positive projection algorithms are suggested, one based on minimizing Euclidean distance and the other on minimizing the divergence of the original data matrix and its non-negative approximation. Experimental results show that P-NMF derives bases which are somewhat better suitable for a localized representation than NMF.