Nonnegative matrix factorization and its applications in pattern recognition

@article{Liu2006NonnegativeMF,
  title={Nonnegative matrix factorization and its applications in pattern recognition},
  author={Weixiang Liu and Nanning Zheng and Qubo You},
  journal={Chinese Science Bulletin},
  year={2006},
  volume={51},
  pages={7-18}
}
Matrix factorization is an effective tool for large-scale data processing and analysis. Nonnegative matrix factorization (NMF) method, which decomposes the nonnegative matrix into two nonnegative factor matrices, provides a new way for matrix factorization. NMF is significant in intelligent information processing and pattern recognition. This paper firstly introduces the basic idea of NMF and some new relevant methods. Then we discuss the loss functions and relevant algorithms of NMF in the… 
Non-negative matrix factorization using constrained optimization with applications
TLDR
This research work provides a new method for solving non-negative matrix factorization (NMF) problems, which has applications to image processing, text clustering and data mining and a new alternating optimization method is proposed.
Robust Kernel Nonnegative Matrix Factorization
TLDR
Compared with the standard NMF algorithm, the new robust kernel NMF updating algorithm is as elegant and as simple, but with the newly added robustness to handle significantly corrupted datasets because of using L2, 1 norm.
Affine Transformation based Nonnegative Matrix Factorization
TLDR
A methodology for document clustering based on the nonnegative matrix factorization (NMF) in affine space is presented, and some algorithms in which the column sums of H is restricted to be one, then the factorization is affine invariant, thus extending the applicable range of NMF methods.
A Novel Fast Non-negative Matrix Factorization Algorithm and Its Application in Text Clustering
TLDR
This new method, with comparable complexity as the priori schemes, is efficient in enhancing nonnegative matrix factorization and achieves better performance in NMF based text clustering.
Supervised Classification of Texture Patterns with Nonnegative Matrix Factorization
  • Rafal
  • Computer Science
  • 2011
TLDR
This paper applies interior-point and active-set methods for estimating the nonnegative factors in NMF and demonstrates a high efficiency of the discussed approach with supervised classification of texture patterns.
Nonnegative matrix factorization: When data is not nonnegative
  • Siyuan Wu, Jim Wang
  • Computer Science
    2014 7th International Conference on Biomedical Engineering and Informatics
  • 2014
TLDR
A new variations of the popular nonnegative matrix factorization (NMF) approach to extend it to the data with negative values by developing a new method that only allows W to contain nonnegative values, but allows both X and H to have both nonnegative and negative values.
Advances in Nonnegative Matrix and Tensor Factorization
TLDR
This issue focuses on the most recent advances in NMF/NTF methods, with emphasis on the efforts made particularly by the researchers from the signal processing and neuroscience area, and reports novel theoretical results, efficient algorithms, and their applications.
Max-min distance nonnegative matrix factorization
Robust nonnegative matrix factorization using L21-norm
TLDR
This paper proposes a robust formulation of NMF using L21 norm loss function and derives a computational algorithm with rigorous convergence analysis that provides very efficient and elegant updating rules.
...
...

References

SHOWING 1-10 OF 65 REFERENCES
Introducing a weighted non-negative matrix factorization for image classification
Improving non-negative matrix factorizations through structured initialization
Algorithms for Non-negative Matrix Factorization
TLDR
Two different multiplicative algorithms for non-negative matrix factorization are analyzed and one algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence.
Non-negative Matrix Factorization with Sparseness Constraints
  • P. Hoyer
  • Computer Science
    J. Mach. Learn. Res.
  • 2004
TLDR
This paper shows how explicitly incorporating the notion of 'sparseness' improves the found decompositions, and provides complete MATLAB code both for standard NMF and for an extension of this technique.
Document clustering based on non-negative matrix factorization
TLDR
This paper proposes a novel document clustering method based on the non-negative factorization of the term-document matrix of the given document corpus that surpasses the latent semantic indexing and the spectral clustering methods not only in the easy and reliable derivation of document clustered results, but also in document clusters accuracies.
FISHER NON-NEGATIVE MATRIX FACTORIZATION FOR LEARNING LOCAL FEATURES
TLDR
A novel subspace method called Fisher non-negative matrix factorization (FNMF) for face recognition is proposed, which results in the novel FNMF algorithm and is shown to achieve better performance than LNMF.
Optimality, computation, and interpretation of nonnegative matrix factorizations
TLDR
The theoretical Kuhn-Tucker optimality condition is described in explicit form and a number of numerical techniques, old and new, are suggested for the nonnegative matrix factorization problems.
Non-negative matrix factorization for visual coding
TLDR
This paper combines linear spun coding and nonnegative matrix factorization into sparse non-negative matrixfactorization, which can learn much sparser representation via imposing sparseness constraints explicitly and can learn parts-based representation via fully multiplicative updates.
Relative gradient speeding up additive updates for nonnegative matrix factorization
...
...