# 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…

## 83 Citations

Non-negative matrix factorization using constrained optimization with applications

- Computer Science
- 2015

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

- Computer Science2012 IEEE 12th International Conference on Data Mining Workshops
- 2012

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

- Computer Science2019 International Conference on Fuzzy Theory and Its Applications (iFUZZY)
- 2019

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

- Computer ScienceICSI
- 2010

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

- Computer Science
- 2011

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

- Computer Science2014 7th International Conference on Biomedical Engineering and Informatics
- 2014

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

- Computer ScienceComput. Intell. Neurosci.
- 2008

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.

Robust nonnegative matrix factorization using L21-norm

- Computer ScienceCIKM '11
- 2011

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.

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