# Research of SWNMF with New Iteration Rules for Facial Feature Extraction and Recognition

## Abstract

**:**

## 1. Introduction

## 2. Image Preprocessing

#### 2.1. Grayscale Normalization

#### 2.2. Extracting Low-Frequency Information by Wavelet Transform

## 3. SWNMF Method with a New Iterative Rule

#### 3.1. New Iteration Rule

^{t}) for J(v) is constructed as Equation (9), which satisfies the conditions as Equation (11). Meanwhile, v is updated by Equation (12) [25]:

^{t}) is constructed to satisfy the conditions as Equation (11) and J is updated by Equation (12), the objective function J(v) can satisfy the Equation (13), which illustrate that J(v) is a non-incremental and convergent function:

^{t}) as Equation (10) and D(v

^{t}) as Equation (15), we can derive the following:

^{t}) constructed as Equation (9) is proved to satisfy the conditions as Equation (11), meanwhile, v is updated with Equation (12), then Equation (13) can be obtained, which illustrates that the objective function J is non-increasing and convergent.

#### 3.2. Sample Weighting and Sparse Constraints

## 4. Classification Based on a Support Vector Machine

_{th}column value of the category voting matrix, i.e., one ticket is voted for the k column. In contrast, if the sample is determined to be of class q by the classifier, then 1 is added to the the q

_{th}column of the category voting matrix, i.e., one ticket is voted for the q column. The number of columns with the most votes in the statistical matrix is the category number of the sample.

## 5. Experimental Results and Analysis

#### 5.1. Comparision of SWNMF with multiple iteration NMF methods and PCA

#### 5.2. Comparison of SWNMF with CNN

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Abudarham, N.; Shkiller, L.; Yovel, G. Critical features for face recognition. Cognition
**2019**, 182, 73–83. [Google Scholar] [CrossRef] [PubMed] - Hassaballah, M.; Aly, S. Face recognition: Challenges, achievements and future directions. IET Comput. Vis.
**2015**, 9, 614–626. [Google Scholar] [CrossRef] - Ghimire, D.; Lee, J.; Li, Z.N.; Jeong, S. Recognition of facial expressions based on salient geometric features and support vector machines. Multimed. Tools Appl.
**2017**, 76, 7921–7946. [Google Scholar] [CrossRef] - Zhang, L.; Zhang, D.; Sun, M.M.; Chen, F.M. Facial beauty analysis based on geometric feature: Toward attractiveness assessment application. Expert Syst. Appl.
**2017**, 82, 252–265. [Google Scholar] [CrossRef] - Dora, L.; Agrawal, S.; Panda, R.; Abraham, A. An evolutionary single Gabor kernel based filter approach to face recognition. Eng. Appl. Artif. Intell.
**2017**, 62, 286–301. [Google Scholar] [CrossRef] - Xiang, Z.; Tan, H.; Ye, W. The Excellent Properties of a Dense Grid-Based HOG Feature on Face Recognition Compared to Gabor and LBP. IEEE Access
**2018**, 6, 29306–29319. [Google Scholar] [CrossRef] - Ali, N.; Bajwa, K.B.; Sablatnig, R.; Chatzichristofis, S.A.; Iqbal, Z.; Rashid, M.; Habib, H.A. A Novel Image Retrieval Based on Visual Words Integration of SIFT and SURF. PLoS ONE
**2016**, 11, 1–20. [Google Scholar] [CrossRef] [PubMed] - Werghi, N.; Tortorici, C.; Berretti, S.; Bimbo, A.D. Boosting 3D LBP-based face recognition by fusing shape and texture descriptors on the mesh. IEEE Trans. Inf. Forensics Secur.
**2016**, 11, 964–979. [Google Scholar] [CrossRef] - Wang, J.; Zhang, R.; Wu, T.T.; Ok, S.; Lee, E. Face Recognition Based on Improved LTP. ISMEMS
**2017**, 134, 6–10. [Google Scholar] - Tan, X.; Triggs, B. Enhanced local texture feature sets for face recognition under difficult lighting conditions. IEEE Trans. Image Process.
**2010**, 19, 1635–1650. [Google Scholar] [PubMed] - Yaman, M.A.; Subasi, A.; Rattay, F. Comparison of Random Subspace and Voting Ensemble Machine Learning Methods for Face Recognition. Symmetry
**2018**, 10, 1–19. [Google Scholar] [CrossRef] - Admane, A.; Sheikh, A.; Paunikar, S.; Jawade, S.; Wadbude, S.; Sawarkar, M.J. A Review on Different Face Recognition Techniques. Int. J. Sci. Res. Comput. Sci. Eng. Inf. Technol.
**2019**, 5, 207–213. [Google Scholar] - Tatepamulwar, C.B.; Pawar, V.P.; Khamitkar, S.D.; Fadewar, H.S. Technique of Face Recognition Based on PCA with Eigen-Face Approach. Comput. Commun. Signal Process.
**2019**, 810, 907–918. [Google Scholar] - Senthilkumar, R.; Gnanamurthy, R.K. A comparative study of 2D PCA face recognition method with other statistically based face recognition methods. J. Inst. Eng. (India) Ser. B
**2016**, 97, 425–430. [Google Scholar] [CrossRef] - Lee, D.; Seung, H. Learning the parts of objects by non-negative matrix factorization. Nature
**1999**, 401, 788–791. [Google Scholar] [CrossRef] [PubMed] - Lee, D.; Seung, H. Algorithms for non-negative matrix factorization. Adv. Neural Inf. Process. Syst.
**2001**, 13, 556–562. [Google Scholar] - Arefin, M.M.N. Face Reconstruction Using Non-Negative Matrix Factorization and ℓ1 Constrained Optimization. In Proceedings of the 2019 International Conference on Robotics, Electrical and Signal Processing Techniques (ICREST), Dhaka, Bangladesh, 10–12 January 2019; Volume 5, pp. 1–9. [Google Scholar]
- Zhu, J.X.; Hu, H.; He, X. Moving Target Detection Method Based on Non-negative Matrix Factorization of Sliding Window. Comput. Technol. Dev.
**2017**, 27, 20–24. [Google Scholar] - Virtanen, T.; Raj, B.; Gemmeke, J. Active-set Newton algorithm for non-negative sparse coding of audio. IEEE Int. Conf. Acoust. Speech Signal Process.
**2017**, 1, 3092–3096. [Google Scholar] - Sabzalian, B.; Abolghasemi, V. Iterative Weighted Non-smooth Non-negative Matrix Factorization for Face Recognition. Int. J. Eng.
**2018**, 31, 1698–1707. [Google Scholar] - Cui, G.; Li, X.; Dong, Y. Subspace clustering guided convex nonnegative matrix factorization. IEEE Trans. Signal Process.
**2018**, 292, 38–48. [Google Scholar] [CrossRef] - Song, H.A.; Kim, B.K.; Xuan, T.L.; Lee, S.Y. Hierarchical feature extraction by multi-layer non-negative matrix factorization network for classification task. Neurocomputing
**2015**, 165, 63–74. [Google Scholar] [CrossRef] - Wang, D.; Gao, X.; Wang, X. Semi-Supervised Nonnegative Matrix Factorization via Constraint Propagation. IEEE Trans. Cybern.
**2016**, 46, 233–244. [Google Scholar] [CrossRef] [PubMed] - Lin, Q.; Li, J.; Yong, J.P.; Liao, D.A. Improved face recognition method based on NMF. Comput. Sci.
**2012**, 39, 243–245. [Google Scholar] - Blondel, V.; Ho, N.D.; Dooren, P.V. Algorithms for Weighted Non-Negative Matrix Factorization. Submit. Publ.
**2007**, 3, 1–13. Available online: https://www.ime.usp.br/~jstern/miscellanea/seminario/Blondel10.pdf (accessed on 3 February 2019).

**Figure 1.**Wavelet transforms of one-layer and two-layer, respectively. The transform results should be listed as: (

**a**) Description of one-layer wavelet transform; and (

**b**) description of the two-layer wavelet transform.

**Figure 2.**Visual images of the optimal base matrices of the various NMF methods. (

**a**) Description of the base matrix image for PCA; (

**b**) description of the base matrix image for threshold SNMF; (

**c**) description of the base matrix image for CNMF; (

**d**) description of the base matrix image for Multilayer-NMF; and (

**e**) description of the base matrix image for SWNMF with new iterative rules.

**Figure 4.**Continuous variation of recognition rate for JAFEE database with increasing r for five methods.

**Figure 9.**Different facial expressions of the same person are correctly recognized. (

**a**) Description of the correct recognition result for one kind of facial expression of ORL data set; and (

**b**) Description of the correct recognition result for another kind of facial expression of ORL data set. (

**c**) Description of the correct recognition result for one kind of facial expression of JAFEE data set; (

**d**) Description of the correct recognition result for another kind of facial expression of JAFEE data set.

r | 20 | 35 | 55 | 75 | 175 | 200 |
---|---|---|---|---|---|---|

SNMF | 81% | 85% | 90% | 88% | 84% | 80% |

SWNMF | 83.5% | 90% | 92% | 95% | 98% | 98% |

Iteration Numbers | Recognition Rate | Recognition Time |
---|---|---|

200 | 2.5% | 55 s |

1000 | 76% | 270 s |

2000 | 84% | 520 s |

Recognition Rate | Recognition Time | |
---|---|---|

SWNMF | 98% | 89 s |

CNN | 84% | 520 s |

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**MDPI and ACS Style**

Zhou, J.
Research of SWNMF with New Iteration Rules for Facial Feature Extraction and Recognition. *Symmetry* **2019**, *11*, 354.
https://doi.org/10.3390/sym11030354

**AMA Style**

Zhou J.
Research of SWNMF with New Iteration Rules for Facial Feature Extraction and Recognition. *Symmetry*. 2019; 11(3):354.
https://doi.org/10.3390/sym11030354

**Chicago/Turabian Style**

Zhou, Jing.
2019. "Research of SWNMF with New Iteration Rules for Facial Feature Extraction and Recognition" *Symmetry* 11, no. 3: 354.
https://doi.org/10.3390/sym11030354